Physics 15b Lab 2: Current, Ohm's Law, Resistance, EMF

Physics 15b Lab 2: Current, Ohm’s Law, Resistance, EMF

In Chapters 1-3 of Purcell, the potentials and fields associated with stationary charges were studied. Chapter 3 allowed charges to move freely in conductors, but the resulting potentials and electrical fields were only evaluated after the charges stopped moving. Chapters 1-3 were the subject of the previous lab. Chapter four, which considers moving charges, is the basis for this lab.

Conductivity as a macroscopic property of materials that depends upon the number of free charge carriers in a material and on the collisions experienced by the charge carriers as they move through the material. The resistivity and conductivity of various materials is presented in table 4.1. The number of free charge carriers in a metal is fixed. The number of free charge carriers in a semi conductor can be increased by doping, or by increasing the temperature of the material. The number of free charge carriers in a neutral gas can be increased by ionizing gas atoms, a process that is used in Geiger counters and neon signs. http://en.wikipedia.org/wiki/Neon_lamp. This lab will consider the temperature dependence of conductivity, as well as the effect of doping, temperature, and ionization on the number of free charge carriers. Just as the concept of capacitance underlies circuit element known as the capacitor, the concept of conductivity underlies the circuit element known as the resistor. The current, I, flowing through a resistor with resistance R is a linear function of the voltage, V, across the resistor where I=V/R. Many important systems have current to voltage relationships that are highly non-linear. Sparks and arcs are particularly dramatic manifestations of non-linear current to voltage relationships. This lab will consider systems with non-linear current to voltage relationships, where the non-linearities have different origins.

Not only can current be a non-linear function of voltage, but the magnitude of the current can also depend on the sign of the voltage; therefore, the I/V for a positive voltage may be different from I/V for the corresponding negative voltage. To study such effects, you will measure the response of a system when charge is sent through the system in one direction and then the response when charge is sent through the same system in the opposite direction. If space is uniform, changing the sign of the voltage applied across a circuit element is the same as keeping the sign of the voltage the same, but reversing the direction of the device. As shown below, if the device is uniform reversing the device has no effect on the experiment at all. If the device is uniform, leaving the device fixed, but reversing the voltage results in a current that is also reversed; however, the ratio of I to V for the reverse voltage is exactly the same as for the case where the voltage went in the forward direction as long as the rest of the space is symmetric. In contrast, if the device is not uniform, then changing the sign of the voltage can make a physical difference. Purcell often stresses the role of symmetry in limiting what is physically possible (e.g. symmetry requires that the electric field of a spherical object have only a radial component), and much of modern physics studies and exploits different sorts of symmetries. Checking whether the response of a circuit to a voltage Vo>0 differs from its response to –Vo is a very simple example of a measurement that probes symmetry by reversing the direction of a potential and measuring the response of the system to the reversed potential.

The current is not always a unique function of the voltage: in some cases, the

same voltage can produce different currents. A system is hysteretic if its response to a stimulus depends on the history of the system, not just the present value of the stimulus. Biological systems can be hysteretic. Systems that experience avalanches are also hysteretic. Memories require hysteresis, and ferromagnetic systems are used in magnetic memories precisely because of their strong hysteretic properties. Thermostatic temperature control systems and battery rechargers are hysteretic, and their energy efficiency depends on how hysteretic they are. The hysteresis in battery charging is an important issue that has limited the successful exploitation of solar energy. Hysteresis can destabilize systems: factors affecting global warming show destabilizing affects. Hysteresis is also exploited to stabilize systems by making them less sensitive to noise. In this lab you will consider at least one hysteretic system. Current, voltage, energy, and power are not only interesting as basic science topics, they also play a significant role in public policy: energy generation and use are becoming subjects of vigorous debates for a number of reasons including national security and climate change. The relationships between current, voltage, energy, and power impose significant constraints on how much electrical energy efficiency can be achieved. Lighting consumes a large fraction of the electrical energy in the United States. At present, a large fraction of our lighting comes from incandescent light bulbs that are very energy inefficient. Australia is already banning incandescent light bulbs. Two alternatives are fluorescents lights and light emitting diodes LEDs. LED’s consist of an n doped semiconductor next to a p doped semiconductor, where a voltage source does work to move charge up the potential hill generated by the internal electric field of the LED. That potential energy is released in the form of light. The use of compact

fluorescent light bulbs and LED’s is being heavily promoted. It has been suggested that if all of the incandescent light bulbs in the US were switched to LEDs, the US could lower its electrical energy consumption by approximately 30%. In this lab, you will consider how the current to voltage relationships for conductors, semiconductors, and plasmas determine the efficiency with which incandescent light bulbs, LEDs, and fluorescent light bulbs convert electrical energy to light. You will also consider some of the spectral and temporal properties of the light that is produced, as well as the power conversion efficiency.

A consequence of the definition of temperature is that

where ν is the frequency, T is the temperature in degrees Kelvin, h is Planck’s constant, and c is the speed of light. This distribution is illustrated in an applet. Figures from the applet are shown on the left below, where the red curve shows the intensity as a function of wavelength with a rainbow in the back showing the positions of various colors of visible light. The corresponding temperatures are shown in pink. The vertical scale is the same on all of the graphs, so the decrease in intensity with temperature can be clearly seen. The figure below shows the measured intensity of the light emitted from the sun, where the yellow corresponds to the spectrum measured at the top of the atmosphere and the red corresponds to a measurement made at sea level. The black lines shows the blackbody spectrum for a temperature of 5250 C.

. http://en.wikipedia.org/wiki/Solar_radiation People like light that has approximately the same color distribution as sunlight and are less happy when there are significant deviations. Light is emitted by an incandescent light bulb when its filament is made sufficiently hot that it emits visible light with a spectrum similar to sunlight, so people like incandescent illumination; however, the process is very energy inefficient. In fluorescent lights, charged particles that are accelerated by an electrical potential collide with atoms, so the electrical potential is doing work to accelerate the charge particles. The collisions between the charged particles and the atoms leave in an excited state. The atoms emit light when they decay from the excited state to which they were transferred by the collisions. The emitted light is in the UV, so a third step is required to convert it to visible. The white lining inside a fluorescent light absorbs the UV and reemits it at a variety of frequencies; therefore, the light emitted from a fluorescent bulb consists of many narrow lines distributed over the visible spectrum.

Thus, the conversion of electrical energy to light is a three step process; however, fluorescent lighting generates much less wasted heat than incandescent lighting. LED’s use electrical energy to do work that increases the potential energy of charges. Light is emitted when the charges suddenly give up the potential energy that they gained from the electrical work. In this process, the electrical energy does work directly on the charges that emit the light rather than accelerating charges that then excite atoms as in fluorescent lights. The energy efficiency of LEDs is significantly higher than for fluorescent lights. Pre-lab Questions: 1. Consider an Ohmic system (V=IR), where V=VoCos[wt]. Plot V as a function of time for t between from 0 to 2 (2 Pi)/w. Plot I as a function of time for t between from 0 to 2(2 Pi)/w. What is the ratio of I(t) to V(t) ? Make an x y graph, consisting of a series of points with an x value given by V(t) and a y value given by I(t) Hint: This is just I vs V since y= I(t) =V(t)/R=x/R. Bonus: Consider a system with V=VoCos[wt] and I= (Vo/R) Sin[wt] as determined by a system that takes data for t between from 0 to 2 (2 Pi)/w. This is a system where the current is proportional to the voltage, but there is a phase lag between them. Such systems will be discussed in detail in Chapter 8 of Purcell and one example is given in a bonus experiment in this lab. 2. Consider an electric heater with a metallic heating element. When the heater is first turned on, the heating element is cold and the resistance of the heater is Rcold. If a constant voltage V is applied across the heater, what is the current that flows through the cold heating element? If the voltage across the heater remains fixed, does the current increase, decrease or stay the same as the heater warms up? Is I(V) a function (that is, given a value of V is the value of I uniquely determined by V)? If you quickly turn off the heater and then turn it on again, is the current just after the heater is turned on larger, smaller, or the same as the current flowing when you first turned on the cold heater. Bonus: Give an example of a system with hysteresis that is not a magnetic memory. 3. To understand a PN diode, it is useful to think about a fish tank with a central divider, where the left side is full of red water and the right side with blue water. This is illustrated on the left below. If the divider is removed, the red water will begin to diffuse from right to left and the blue water will move from left to right. This is how cream mixes into coffee if the coffee is not stirred. The net result is a mixed region, as shown on the right. In the PN diode case, it is the positive charges from the P doped region that move into the N doped region and the electrons from the N doped region that move into the P doped region. The free charge carriers in the N doped region are electrons. The free charge carriers in the P doped region are called holes.

A cartoon of the process is shown in this applet http://jas.eng.buffalo.edu/education/pn/pnformation2/pnformation2.html (Note the menu at the right side offers a heading called “introduction” that explains the applet). Both the N and P regions were originally electrically neutral; therefore, diffusive motion of the charges results in the N doped region acquiring a net positive charge and the P doped region a net negative charge. These net charges produce an electric field that

opposes the diffusive motion. The system rapidly approaches equilibrium, and the average charge distribution becomes time independent. The resulting free charge carrier density as a function of position, net charge distribution as a function of position, electric field as a function of position, and potential as a function of position are shown in the image below from Wikipedia. http://en.wikipedia.org/wiki/P-n_junction The area labeled “space charge zone” corresponds to the depletion zone because the density of free charge carriers in that region is depleted in comparison with the density in the neutral regions. There is almost no free charge in the depletion zone; therefore, when the size of the depletion zone is large the two sides of the diode behave as if there were no conducting path connecting them. In this case, the diode could be approximated by a single pole single throw switch in the open position where no charge can pass through the switch.

So far, we have considered the charge distribution and electric field in the diode when there is no potential difference applied across the diode. If one applies a voltage across the diode, the charge distribution inside the diode changes. If a sufficiently large positive voltage is applied across the diode, the depletion zone disappears and free charge can easily move through the diode. In this case, the diode could be described as a closed single pole single throw switch in series with a battery and a small internal resistance, as illustrated below. In the illustration ,the top line shows the internal structure, the line below it shows the circuit symbol for the diode in the same orientation, and the two final lines show the approximate equivalent circuits, where one applies when the voltage across the diode is less then Vthreshold and the other applies when the voltage is greater then Vthreshold.

Illustrate the size of the depletion zone, and include arrows illustrating the magnitude and direction of the electric field in the depletion zone and the direction of the current flow in the depletion zone for a PN diode for four applied voltage differences: 1. Vo=0, Vo=0.6 V, Vo=-2. Sketch I vs V for a Si diode for voltages from -1 V to 1 V. Label the regions corresponding to a reverse bias, a small forward bias, and a large forward bias. Bonus: Sketch V/I(V) as a function of V. If the diode were an ohmic device with resistance R, this plot would be a constant with a value equal to the resistance R. The plot for the diode is not constant, so the diode is not ohmic; however, the value of V/I(V) could be interpreted as a voltage dependent resistance. Bonus: The Shockley equation for the current in a diode as a function of V, the voltage across the diode, is approximately given by I= isat (Exp[V/VT]-1), where VT= k T/e is the ratio of the thermal energy a a temperature T to the charge of the electron. Note: k is Boltzmann’s constant= 1.38x10-23 j/K and Vthresh is the threshold voltage for the material. Isat varies widely from 10-8 to 10-14 amps, but choose 10-12 as a value. Plot I vs V for a diode at room temperature (T=300 K) for voltages from -1 V to 1 V. The following websites offer useful information for this problem. You can cut and paste images from a website to answer questions, but you must provide explanations of the images. http://electronics.howstuffworks.com/led.htm/printable http://en.wikipedia.org/wiki/Diode http://jas.eng.buffalo.edu/education/pn/biasedPN2/BiasedPN2.html http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/diode.html ; (Note at V=0 question marks appear next to the depletion region diffusion current and drift current. If you click on a question mark, an additional explanation appears and the red rectangles highlight the representations of that quantity in the applet. Also note that the charge flows shown by the dots are for electrons, which are negative charge carriers) http://jas.eng.buffalo.edu/education/pn/biasedPN/index.html Bonus: Why does the drift current independent of voltage for voltages less than -1 V? Bonus: Why are diodes capacitive? Hint: http://jas.eng.buffalo.edu/education/pn/cv/index.html 4. For a voltage as a function of time given by 170 Cos [2 pi 60 t], what is the RMS value of the voltage? For a system that delivers electrical power with an RMS voltage of VRMS, explain why the average power consumed by a device with resistance R that is

connected to this power source is simply VRMS R. What the potential difference between ground and neutral at a breaker box? 5. What is the Thevenin equivalent resistance of a series combination of R=100 Ohms and R=1010 Ohms? If the voltage difference across the series combination is V, what is the current flowing through the series combination. If there is a voltage difference V across the series combination of 100 Ohms and 1010Ohms, what is the approximate voltage difference across each of the two resistors? If there is voltage V across a series combination of R=100 Ohms and R=0.01 Ohms what is the voltage difference across each resistor? 6. Consider a device with a voltage dependent resistance such that R= 1010 Ohms if the potential difference across the device is less than 0.6 V, and R=0.01 Ohms if the voltage is more than 0.6 V. Let the voltage difference across the device be V=2 Cos[wt]. Plot the voltage across the device as a function of time. Draw vertical lines at the times when the V=0.6 V. Shade the areas of the graph where V>0.6 V. Plot the resistance as a function of time on the same graph. What is the current flowing through a resistor with R= 1010 Ohms if the voltage difference across is 2V? What is the current flowing through a resistor with R= 0.01 Ohms if the voltage difference across is 2V? Plot I(t), the current flowing in the circuit as a function of time for t between from 0 to 2 (2 Pi)/w. Bonus: Consider a device with a voltage dependent resistance such that R= 1010 Ohms if the potential difference across the device is less than 0.6 V, and R=0 Ohms if the voltage is more than 0.6 V. Let the device be connected in series with a 100 Ohm resistor. The voltage difference across the series combination is V=2 Cos[wt]. Plot this voltage difference as a function of time. Draw the Thevenin equivalent resistance of the series combination as a function of time on the same graph. Plot I(t), the current flowing in the circuit as a function of time for t between from 0 to 2 (2 Pi)/w. Plot the voltage across the 100 Ohm resistor as a function of time. Bonus: Consider a diode in series with a 100 Ohm resistor. Use the equivalent diode model given in problem 3 to plot V(t) for the signal generator output, the diode and the resistor on the same plot. Plot I(t) for the circuit. Plot I vs the voltage across the resistor for voltages from 0 to 1. Plot I vs the voltage across the diode for voltages from -1 to 1 V. Bonus: Consider a power system that must deliver a fixed power P. This power must be transmitted over an electrical cable characterized by a resistance R. Express the energy lost in transmitting electricity through the system in terms of P, R, and the voltage V at which the power is delivered. Note, the US is pushing for higher power line transmission voltages and high temperatures superconductors to reduce energy losses in power transmission. Bonus: Consider the circuit below. At times t<0, let the switch be connected to the left side, so that the capacitor is charged by the battery, as shown in the diagram on the left below. Assume that the system has reached equilibrium by t=0. At t=0 flip the switch so it is connected on the right, as shown in the diagram on the right below. What is the voltage across the capacitor as a function of time for t>0?

7. What is the origin of the difference between the yellow and red curves in the solar radiation graph above that was copied from Wikipedia and included in the introduction to this lab? What is the origin of the narrow spikes of reduced intensity in the red curve?

8. Draw the electrical schematic drawing corresponding to the breadboard circuit shown above. Assume both resistors have the same resistance R and that the power supply has a potential difference V.

Bonus: Assume that you want to measure the current that flows in a device as a function of the voltage applied across the device. This is called an IV curve. A circuit for such a measurement is shown in the figure on the left above, but to make the measurement you need some way to the measure the voltage across the device and the current flowing through the device. The diagram in the center shows an appropriate circuit, where the A

in the circle represents and ammeter and the V in the circle represents a voltmeter. Unfortunately, adding them perturbs the circuit. The new circuit is shown on the right above where R1 is the resistance of the ammeter and R3 is the resistance of the voltmeter. The perturbation does not significantly affect the experiment if R1<<R2 <<R3. Let R1= alpha R2 and R3= R2/beta, where alpha and beta << 1. Show that the IV curve for R2 can be approximated by I1/V3= (V1/R1)/V3, where to first order in alpha and beta the ratio of the measured IV to the true IV is (1+beta), independent of alpha. (Hint: Apply Kirchoff’s Laws with R1 and R3 expressed in terms of R2) Circuit schematics will be used extensively in this lab, so a table of circuit symbols is provided below.

Lab Goals 1. Study the influence of voltage, electric fields, and collisions on charge

propagation and explore the limitations of Ohm’s Law 2. Study the influence of charge carrier density on conductivity. 3. Study energy transfer and power consumption in electrical systems. 4. Study charge propagation in semi-conducting materials, including diodes formed

by combining an n-type semiconductor with a p-type semiconductor. 5. Study parity detection and hysteresis in simple systems 6. Learn how to assemble temporary circuits 7. Discover some effects of apparatus choice on data acquisition and measurement 8. Study effects of combining resistors and capacitors 9. Practice with the correspondence between circuit schematics and actual circuits 10. Learn about the form in which electrical power is distributed in the United States 11. Study the mechanisms underlying the generation of light from electrical power,

including the detailed emission properties and energy efficiency of different electrically driven light sources.

1. Relationships between Voltage and Current

Goals: Determine the current to voltage relationships for a 150 Ohm resistor, an LED, and light bulb. Understand the basic mechanisms that govern IV relationships, and consider symmetry and hysteresis as they apply to light emitting devices. Study the power consumption of the devices. Measure the relative energy efficiency of the LED and the light bulb.

a. Materials: 150 Ohm resistor; 100 Ohm Resistor ; 1 BNC T ;1 BNC to banana;4 BNC cables;4 micrograbber to BNC; function generator; multimeter

Measure the IV (current to voltage) curve for a 150 Ohm resistor using the function generator as a voltage source for a voltage range of +-5V. You could use a source with a voltage that is constant as a function of time, but this is very tedious. You can use the signal generator to produce a voltage that changes slowly with time. If the change is slow enough, the circuit will be in equilibrium, so you can apply the results from Chapter 4 to the IV relationships. Thus, you can measure the IV curve by changing V with time and measuring the resulting current as a function of time.

Apparatus Assembly Directions

1. Setup the scope to monitor the signal generator

a. Connect the BNC T shown on the left above to the output of the signal generator that is highlighted by the light blue arrow in the image in the center above.

i. The T is used to convert a single BNC jack to two jacks, so that two BNC cables can be connected to the same output as shown in the image on the right above.

b. Make sure that none of the buttons highlighted by the purple rectangles depressed. If any are, press on the button and it should pop out.

2. Setup the signal generator to produce a 5 V amplitude triangle wave at 20 Hz a. Turn on the signal generator on by pressing the button highlighted by the

purple arrow. b. Connect the output of the signal generator to CH1 on the scope using a BNC

cable connected to one side of the BNC T on the output of the signal generator. c. Choose the triangle wave output by depressing the button indicated by the

pink arrow. d. Use the signal on the scope to adjust the signal generator to produce a triangle

wave with a 5 Volt amplitude and a 20 Hz frequency. The amplitude is controlled by the knob highlighted by the yellow circle. Get the 20 Hz frequency by pressing the 100 Hz frequency choice button ( indicated by the dark green arrow) and tuning the coarse frequency adjustment knob(highlighted by the red circle) until the frequency display reads 20 Hz. If the displayed frequency changes by more than 1 Hz after you have let go of the knob for more than 10 seconds, then ask for assistance.

3. Connect the circuit

a. Place the 150 Ohm resistor in the breadboard b. Connect the Logger Pro current sensor in series with the resistor, as shown in

the schematic and image above c. Connect a second BNC cable to the BNC T on the output of the signal

generator. The picture on the left above shows the signal generator with the BNC T connected, and two cables coming out from the sides of the T.

d. Connect a jack/micrograbber combination to the end of this BNC cable, and then use the micrograbbers to connect the voltage source in parallel with the

series combination of the resistor and the current sensor, as shown in the schematic and image above.

e. Connect a Logger Pro voltage sensor in parallel with the resistor. Use the voltage probe with the wires permanently attached to the alligator clips. Place each of the wires in the voltage sensor alligator clips into a hole in the same column as each of the two resistor lead wires as shown in the image above.

4. Setup Logger Pro to acquire data a. Make sure the spectrometer is NOT connected to the USB port on the

computer. If it is connected, it will make data acquisition extremely slow. b. Make sure that the LabPro Box is connected to the USB input on the computer. c. Connect the LoggerPro probes to the LabProb Box.

i. Connect the LoggerPro voltage probe with the alligator clips that are permanently clamped around wires to the input of channel 3 on the LabPro Box.

ii. Connect the voltage probe with the unmodified alligator clips to the input of channel 1 on the LabPro Box.

iii. Connect the current sensor to the input of channel 2 on the LabPro Box.

d. Start IV Template.cmbl. This is a LoggerPro program that will assist you in taking data. This program should be on the desk top, but if it is not you can download it from the 15b website. A screen shot of the program is shown below. The image on the left includes annotation on the significance of each window. The image on the right shows typical data, including a linear fit to the IV curve.

Meaning of the program display

e. The upper left box shows the voltages as a function of time. For section 1a you are using only 1 voltage probe, and its output should be on channel 3. The output channel 3 is plotted in green, and the output of channel 1 is plotted in red. The voltage for channel 1 should always be zero for section1a.

f. The lower left box shows the current as a function of time. This should appear in column 2.

g. The box in the center of the top row shows a plot of the current flowing through the resistor, IR, as a function of the voltage across the resistor, VR.

h. The superimposed dialog plot gives the linear fit parameters for IR vs VR. i. The other plots are not used in section 1a.

5. Tune the signal generator to the setting for data acquisition and begin data acquisition

a. Set the signal generator to 0.2 Hz by depressing the 1 Hz frequency button highlighted by the bright green arrow. Do not change the frequency adjustment knobs. The frequency display sometimes shows odd values at these low frequencies, but the signal generator output should be at 0.2 Hz.

b. Start data acquisition. c. Measure the IV curve for a 0.20 Hz triangle wave. The data should resemble

the window on the upper right. 6. Troubleshooting: Skip this if everything is working.

i. If the scaling on the graphs is bad 1. You may want to rescale some of the curves so that they

occupy most of the space in the graph, making them easier to read. Try autoscaling first. To get autoscale right click on the window and choose autoscale. If LoggerPro makes bad choices using autoscale, rescale the plot

ii. If the current is not appearing on CH2 or the voltage across the resistor is not appearing on Ch3, then do the following.

1. Quit LoggerPro 2. Correct the connections to the LabPro Box so the current is on

CH2 and the voltage across the resistor is on channel 3. The other voltage probe should be connected to CH1, but not measuring anything. Restart IV Template.cmbl. If the data acquisition still not working, please ask for immediate assistance.

Is the resistor ohmic? Calculate the effective resistance as a function of voltage. Hint: If you click on the IV curve, then choose “Analyze” from the toolbar, a dropdown menu will appear. Choose linear fit, and a LoggerPro will calculate the slope and intercept of the line and print the values in the window. How does the measured resistance compare with the nominal resistance? Is the device symmetric? Is it hysteretic? Note: you would get the same results for a 20 Hz triangle wave. Bonus: Repeat with a 20 Hz triangle wave.

b. Materials: Light Bulb, signal generator;scope;BNC T ; BNC to banana; micrograbber/BNC jacks and BNC cables; photodiode;multimeter


1. Setup to apparatus to monitor the IV curve a. Replace the 150 Ohm resistor with the light bulb by removing the resistor and placing the light bulb leads in the same breadboard holes that were occupied by the resistor. An image of the light bulb is shown above on the left. The new circuit diagram is shown in the center of the figure above.

2. Setup the light collection a. Connect the photodiode to the LoggerPro voltage probe by clipping the

alligator connectors to the leads of the photodiode. A photograph of the photodiode is shown at the far right.

b. Place the photodiode so that the black surface is facing the light bulb. The photograph is actually of the back of the diode.

c. Hold the photodiode just above the surface of the light bulb and keep it there during data collection.


a. Make sure the signal generator is set 0.2 Hz and start data acquisition. b. Start IV Template.cmbl. A screen show is shown below. The image on the

left includes annotation on the significance of each window. The image on the right shows typical data, with directional arrows drawn in to indicate which curve corresponds to x axis values that are decreasing the time and which corresponds to x axis values that are increasing with time.


1. The upper left box shows the voltages as a function of time. a. The green line shows the voltage across the light bulb b. The red line shows the voltage from the photodiode. This signal is

proportional to the intensity emitted by the light bulb. 2. The lower left box shows the current as a function of time. 3. The box in the center of the top row show a plot of the current flowing

through the light bulb, Ibulb, as a function of the voltage across the light bulb, Vbulb. as a function of voltage

4. The upper right box shows the intensity emitted by the bulb as a function of the voltage difference across the bulb

5. The central box in the lower row shows the intensity emitted by the bulb as a function of the current flowing through the bulb,Ibulb.

6. The lower right hand box shows the intensity emitted by the bulb as a function of the product VR and IR.

c. Troubleshooting: Skip this if everything is working. i. If the diode voltage becomes increasingly negative as the light

intensity increases and you would prefer the voltage to become more positive, reverse the connection between the voltage probe and the leads to the photodiode. This should make the voltage increase with increasing intensity.

Measure the IV curve for a 0.20 Hz triangle wave while measuring the voltage on the photodiode at the same time. The voltage on the photodiode is proportional to the intensity falling on it, so the voltage is proportional to the emitted intensity. Is the light bulb ohmic? Is the device symmetric? Is it hysteretic? What is the voltage across the light bulb when it begins emitting light? What is the voltage across the light bulb when it stops emitting light? For currents where the bulb is emitting light, what is the slope of the intensity vs current curve when the current is increasing with time? Is the slope as a function of current for the case where the current is decreasing with time higher or lower than the case when the current is increasing with time? Explain your result. How many light pulses does the light bulb emit during one voltage cycle? Is the intensity a linear function of electrical power? For voltages where the light bulb does emit light does the ratio of emitted intensity to electrical power increase or decrease with increasing power? Repeat the

measurement with a 20 Hz triangle wave by pressing the 100 Hz frequency selection button on the signal generator. Explain any differences between the 20 Hz measurement and the 0.2 Hz measurement.

c. Materials: LED (Light Emitting Diode); 100 Ohm resistor;tunable voltage

source; current and voltage monitors; photodiode;1 BNC T ;;4 BNC cables;4 micrograbber to BNC;multimeter


1. Setup to apparatus to monitor the IV curve for a resistor in an RC circuit a. Replace the light bulb with the LED by removing the resistor and placing the light bulb leads in the same breadboard holes that were occupied by the resistor. A schematic and illustration of the new circuit are shown in the next two images. 2. Setup the light collection

a.Place the photodiode so that the black surface is facing the top of the LED. LED emission is quite direction, so plcing it on top is important. b. Hold the photodiode just above the surface of the light bulb and keep it there during data collection.


d. Make sure the signal generator is set 0.2 Hz and start data acquisition using IV Template.cmbl.

Measure the IV curve for a 0.20 Hz triangle wave while measuring the voltage on the photodiode at the same time. Is it ohmic? Is the device symmetric? Is it hysteretic? What is the voltage across the LED when it begins emitting light? What is the current across the LED when it begins emitting light? How many light pulses does the LED emit during one voltage cycle? For voltages where the LED emits light, does the ratio of the emitted intensity to the electrical power consumed increase or decrease with increasing power? For voltages where the LED emits light, is there a range of current values for which the intensity is a linear function of current? Look at the signal generator output on the scope. Remove the BNC cable that is connected to

the circuit from the BNC Does the signal generator output change when you disconnect the circuit? Why?

Bonus: Diodes are often modeled as a series combination of an ideal diode (R=0 for V>0, R= Infinity for V<0), a battery with a voltage difference equal to the threshold voltage of the diode, and a series resistor. Find the values of the series resistance and the battery for the diode in this experiment. Bonus: Plot Log[I] vs V for the LED. How well does it fit the Shockley mode? Fit the Shockley model parameters. Bonus: Repeat the experiment with a 1k series resistor. Explain the difference between this result and your original result. Bonus: The emitted is almost intensity a linear function of current just above threshold because almost every charge that crosses the junction transfers from the conduction band to the valence band by emitting light. At higher voltages, this process becomes less efficient. Offer some possible mechanisms for this decreased efficiency.

d. Bonus: Overall Questions about the resistor, LED, and flashlight bulb. Please

skip these if you are running short of time. a. In devices with a potential difference V across them that results in

current flow, does the change in kinetic energy of the electron entering and leaving the device correspond to eV? If not, why not. Does this violate conservation of energy?

b. Did the motion of the electrons through the device result in an energy change in the device? If not, where did the energy go. Please answer separately for each device with a discussion of results for different voltages for a given device if applicable.

c. Is there any device to which a voltage can be applied without resulting in power consumption? If so, over what range of voltages results in no energy consumption?

d. Double Bonus: Design an experiment to detect an external electric field. Given the parameters of your experiment, how small a field could you detect?

2. What comes out of the wall?

Goal: Learn about the form in which electrical power is delivered to consumers in the US.

a. Materials: light source box; scope probe; scope; multimeter; wet paper towel Electricity is delivered in the form of an alternating current (AC) signal where the voltage and current vary sinusoidally with time. Different countries have different standards. AC voltmeters read the RMS values of the current and voltage. Ask someone on the laboratory staff to use an AC Voltmeter to measure the voltage difference between the hot, ground, and neutral outputs of a standard duplex wall plug, such as the one shown below. A detailed

discussion of power generation and delivery in the US is given in a supplemental information section. What is the measured voltage difference between hot and ground? What is the measured voltage difference between hot and neutral? What is the measured voltage difference between neutral and ground?

Bonus: Measure the resistance across your body by holding the Ohmeter leads in your hands. Compare to the resistance across one hand. Compare with the resistance across your body when your hands are wet. Compare with the resistance when your hands are wet with salt water. How much current would flow through those three resistive paths if a 110V AC potential was connected to those points on your body. How does this compare with 5 mA, the “safe current?”

b. Materials: Scope; light box, BNC cables, scope probe

The two images above illustrate the connections to the lightbox. For this section of the lab, you will just use the lightbox to monitor the AC voltage coming out of a wall socket. The lightbox just makes this experiment safer.

Apparatus Assembly Directions 1. Setup the scope to monitor the AC voltage coming from the wall using the light

box a. Monitor the voltage difference between hot and ground on Ch1

i. Attach the scope probe to the light box as shown in the image on the right above

1. Attach the scope probe micrograbber to the wire loop inside the box behind the slot. The slot in the lightbox has a wire loop to which the micrograbber on the scope probe can be attached.

a. The wire behind the slot is connected to the hot output of the wall socket; therefore, the central pin of the BNC for the scope probe is attached to the hot voltage coming from the wall.

2. Attach the alligator clip on the scope probe to the ground terminal on the outside of the lightbox.

a. The outside of the BNC is not connected to the ground coming from the wall.

ii. Connect the BNC output of the scope probe to the input of CH1 on the scope.

b. Monitor the voltage difference between neutral and ground on Ch2 i. Connect the BNC jack on the light box that is labeled neutral to

channel 2. a. This jack is connected so its center pin is at the neutral

potential, and the outside of the BNC is at ground. c. Adjust the scope settings so that several cycles of the 60 Hz frequency are

visible on the scope. 2. Finish setting up the light box a and begin data acquisition

a. Plug the cord on the light box directly into the wall socket b. Adjust the voltage scale on the scope so that you can clearly read the signals

on CH1 and Ch2.

Channel 1 shows the difference between hot and ground. How well is CH1 described by V = 170 Sin (2 π 60 t)? How do the measured peak to peak values compare with voltage reading on the AC voltmeter when it was connected between hot and ground? Channel 2 shows the voltage difference between neutral and ground. Is it zero? How can there be a voltage difference between neutral and ground if the two are connected at the breaker box?

3. Efficiency of the conversion of Electrical Power to Light

Goal: Understand the basic mechanisms that transfer electrical energy to optical energy in light sources. Compare the energy efficiency of different electrically powered light sources. Study the properties of the light emitted by the different sources. Divide the class so that at least one group does each of the light sources: 1. incandescent light bulb; 2. compact fluorescent light bulb; 3. LED spotlight. Each group will do the same experiments, but with the different bulbs

a. Materials: light emitter and lightbox;variac; photodiode; spectrometer; temperature sensor; ruler; scope;scope probe;BNC cables, Labview

A schematic of the light box and its connections to the scope are shown in the schematic diagram in the left hand section of the image above. The other two images in the figure show photographs of the wiring inside the box. In the central image, each of the wires is highlighted and labeled, where red is hot, white is neutral, green is ground, and yellow is V3. In the right hand image, the wires are visible. Wires at the hot voltage are shown in red and wires at the neutral voltage are shown in gray.

Apparatus Assembly Directions 1. Setup the scope to monitor voltage across and current flowing through a light

emitter, as well as the intensity emitted. a. CH1 already displays the potential difference between hot and ground as

monitored by the scope probe. This connection is still correct, so no change is required.

b. CH2 already displays the potential difference between neutral and ground. This connection is still correct, so no change is required.

c. CH3 will monitor the voltage across the 1 Ohm resistor that is connected in series with the light emitter.

i. Connect the BNC jack labeled 1 Ohm to the input of CH3 on the scope using a BNC cable. How is this voltage related to the current flowing through the light emitter?

d. CH4 will monitor emitted light by the device, which is proportional to measuring the voltage generated across the leads of the photodiode.

i. Connect a micrograbber to BNC to the leads of the photodiode ii. Connect the jack on the micrograbber to BNC connector to a BNC

cable that is in turn attached to the input of channel 4, so CH4 displays the emitted intensity as a function of time.

iii. Hang the photodiode so that it can measure the light emitted by the light source without your having to hold it. It is convenient to hang the photodiode from a chemistry stand where the diode is approximately 1 cm from the light source. Be careful to avoid saturating the photodiode.

e. Make sure all 4 channels are displayed on the scope.

2. Setup the variac to control the voltage difference between hot and neutral.

a. Connect the plug from the lightbox to the outlet on a variac, and connect the variac to a wall plug. An image of a variac is shown above. The wheel on the top of the variac controls the RMS amplitude of the AC voltage coming out of the variac. You will use the variac to control the RMS voltage suppled to your light box, which in turn controls the voltage across the light emitter.

b. Set the knob so that the line points to 0 volts c. Turn on the variac by flipping the power switch.

3. Begin data acquisition a. Start the Labview program entitled 15b_lighting.vi. It will not acquire data

if all 4 channels are not displayed on the scope. A screen shot is shown below.

Meaning of the items in the program display.

i. The green curve on the left shows the RMS current IRMS flowing through the light emitter as function of VRMS, the voltage across the light emitter. IRMS= (CH3-CH2/1 Ohm) and VRMS is CH1-CH3.

ii. The lavender curve on the right shows the emitted intensity vs the RMS power. b. Begin slowly and smoothly turning the knob on the variac and continue

turning until the knob points to 120 V. DO NOT TURN THE VOLTAGE ABOVE 120V!!! As you turn the knob, you change the voltage supplied to the lightbox. The plots on the program should changes as you turn the knob. When you reach 120 V, the program should display an IV curve for voltages

from 0 to 120 V. It should also display intensity as a function of electrical power for voltages from 0 to 120 V. Turn the voltage slowly and smoothly back down to 0 V and click on the stop button on the program.

Does your device emit light for all input voltages? If not, at what voltage does the device turn on? For voltages where the device emits light, does the intensity increase significantly with voltage? For voltages where the device emits light, does the ratio emitted intensity to electrical power increase or decrease with increasing power. Sketch the relative efficiency of the conversion of electrical power to optical power as a function of applied voltage. Is it linear? Explain your result

Apparatus Assembly Directions 1. Setup the spectrometer to measure the intensity as a function of frequency for

the light emitted by the light sources as a function of the voltage across the light emitter.

a. Disconnect LabPro from the USB connection on the computer. If it remains connected, the spectrometer will not work.

b. Place the spectrometer so the hole is facing the light source. 2. Finish the setup the spectrometer to and begin data acquisition

a. Start the program called light spectrum that should be on the desktop. This program operates the spectrometer for you and displays the resulting data, as shown in the screen shot below.


a. The line shows the intensity as a function of wavelength. The rainbow in the back shows the color that corresponds to each wavelength.

b. Several different spectra can be obtained

The equation above gives the relationship between the temperature of an object and its emission spectrum. The pink curves in the image below the screen shot show the intensity as a function of wavelength for four different temperatures, where again the rainbow shows the color corresponding to that wavelength. As you can see, cooler objects emit light that is redder and less intense than hotter objects. You can use the graphs to estimate temperatures of the light emitters studied in this section.

For comparison, the emission spectrum for the sun is shown in the figures on the left. The top left figure shows the distribution for a temperature approximately equal to the temperature at the surface of the sun. The wavelength scale is much larger, so the

rainbow only occupies a small fraction of the figure. The bottom figure has the same wavelength scale and shows the measured intensity as a function of wavelength for sunlight, where the black curve shows the predicted curve for an object with a temperature of 5250 C. Notice only about 1/3 of the light emitted by the sun falls within the visible wavelengths. Data Taking Steps 1. Turn the Variac to 40 V. Leave the voltage constant. 2. If the light emitter is emitting light, take a spectrum at 40 V. Otherwise skip to step 4. 3. Click on the stop button when you are satisfied with the spectrum. 4. Turn the variac up to 60 V. Leave the voltage constant. 5. If the light emitter is emitting light, take a spectrum at 60 V. Otherwise skip to step 7. 6. Hit the collect button again and choose the option to keep collecting in the same graph. 7. Click on the stop button when you are satisfied with the spectrum. Both spectra should be displayed at the same time. 8. Turn the variac up to 110 V. Leave the voltage constant. 9. Hit the collect button again and choose the option to keep collecting in the same

graph. 10. Click on the stop button when you are satisfied with the spectrum. All 3 spectra should be displayed at the same time.

Does the spectrum of your source change with voltage? How does your measured spectrum the solar spectrum shown above? Is the emitted spectrum well described by a black body at some temperature T? If so, what temperature? If not, what is the origin of the light and what determines its color? Are there any narrow features in the emission spectrum? If so, what is their origin. Bonus: Use the curve fit option to fit the spectrum to a Gaussian. Bonus: For the maximum voltage, measure the photo-detector current as a function of distance from the bulb. Note Solid state temperature sensors exploit the temperature dependence of conductivity. Bonus: 1. measure the angular dependence; 2. calculate the actual total power conversion from electrical power to optical power. Hint: the conversion efficiency of a photodiode is approximately 50 microamps per mW/cm2.

b. Present and explain the results.

4. Bonus: Charging and Discharging a Capacitor Goal: Study the current and voltage as a function of time for an RC circuit, as well as parallel and series combinations

a. Materials: function generator, oscilloscope, breadboard, micrograbber/BNC connectors, BNC cables,two 0.1 microFarad capacitor, 10k Ohm resistor,1 kOhm resistor

In the previous lab, you measured the decay of the RC circuit formed by a 10 microFarad capacitor and the resistor inside the LoggerPro voltage probe and found that the voltage across the capacitor decayed exponentially with time; however, since RC circuits had not yet been covered in class, we did not discuss it as an RC effect. In that lab, you charged and discharged the capacitor using a battery and a single pole double throw switch. In this lab, you will use the square wave from a function generator to change the voltage across the capacitor from +5 V to -5 V . If the frequency of the square wave is slow enough, the RC will have time to reach equilibrium before the square wave changes voltage, so you will be making a DC measurement using something that is really an AC source.

Apparatus Assembly Directions 1. Setup the signal generator to produce a 5 V amplitude triangle wave at 20 Hz

a. Change the signal generator frequency to 20 Hz by pressing the 100 Hz frequency button.

b. Change the signal generator output to a square wave. If the signal on the scope is not a nice clean square wave, then ask a staff member for assistance. It probably means that the input impedance of the scope is set to 50 Ohms and should be changed to 1 MegaOhm.

2. Connect the RC Circuit a. Use the breadboard to connect a 10 k resistor in series with a 0.1 microfarad

ceramic capacitor. Such a ceramic capacitor with axial leads is shown on the left above.

b. Connect the output voltage of the signal generator in parallel with the series combination, as shown in the images above. Make sure the positive voltage (red micrograbber) is connected to the capacitor and the ground (black micrograbber) is connected to the resistor. Note: Channel 1 already displays the voltage across the RC series combination since it is the same as the output of the signal generator.

3. Setup the scope to measure the voltage difference across and current flowing through the RC circuit

a. Channel 1 already displays the total voltage difference across the series combination

b. Channel 2 will monitor the voltage across the resistor. Connect the micrograbbers from a micrograbber to BNC jack in parallel with the resistor, where the black micrograbber is connected to the same end as the black micrograbber from the signal generator. Use a BNC cable to connect this BNC jack to CH2 on the scope so that CH2 displays the voltage across the resistor. How is this related to the current flowing through the resistor? How is this related to the current flowing through the capacitor?

c. The math function will display the voltage across the capacitor. Press the red button highlighted by the red rectangle that is superimposed on the image of the scope that is shown on the left below. Choose “-“ from the function menu so that the red display shows Ch1-Ch2 as shown in the image on the right below. If the menu comes up in FFT mode, press the bottom left menu button that is highlighted by the light green box, and the scope should return to the correct menu. If the channels are wrong, press the menu buttons just to the right of the box showing the channel for the math operation and keep pressing the button until your desired channel appears. Why is Ch1-Ch2 equal to the voltage across the capacitor

d. Adjust the voltage sensitivities on CH1, CH2, and MATH so that they are

the same. e. Adjust the scope settings so that approximately 1 period of the square wave

square wave is displayed. Do the voltages across the resistor and capacitor approach equilibrium during one half cycle of the square wave? Why does this approximate a measurement where the RC is charged and discharged using a switch and a battery?

4. Tune the signal generator to the setting for data acquisition and begin data

acquisition a. Readjust the timescale so that the display for CH1 and CH2 on the scope

resembles the image below.

b. Troubleshooting: Skip this if everything is working.

i. If you cannot get your display to resemble the image shown above, ask for assistance. Instructions are included below should you wish to try on your own.

1. If you keep getting a voltage spike that is negative, then the edge trigger menu is set to trigger on a negative slope rather than a positive slope.

a. Option 1 i. Hit autoset. This will fix the edge trigger

problem, but mess up all of your other settings ii. Fix the voltage and time scales to get the

image above b. Option 2

i. Enter the trigger menu by pushing the button that is highlighted by the yellow rectangle in the image of the scope two figures above.

ii. Choose normal from the right hand menu. iii. Choose slope from the bottom menu. A new

right hand menu should appear, featuring a positive slope and a negative slope.

iv. Pick the icon for positive slope. c. Start the Labview program called 15B_RC.vi. d. Acquire a signal from the scope by pressing the white arrow in the upper left

hand corner of the screen. This launches a process where Labview queries the scope and obtains the voltages as a function of time for each channel. An annotated screen shot is shown in the image on the left below.


a. The upper left window shows the scope trace where CH1 is yellow and CH2 is blue, just as they are on the scope. CH1 is displaying the signal generator voltage, VS, and CH2 is the voltage across the resistor, VR.

i. The small box on the left allows you to average your data. Each point becomes the average of the N time points, where N is the number in the box. If N=1, there is no averaging. If the noise changes rapidly during the time that the signal is effectively constant, then averaging over time removes a lot of noise.

b. The lower left hand window also shows CH2 vs time. i. The small box at the left allows you to choose a linear or log plot,

where 1 gives a log plot and 0 gives a linear plot. ii. The red line shows a linear fit to the plot with a value for the slope

displayed in the window just above the graph. iii. It is possible to restrict the data shown in this window to a only a

portion of the time displayed in the upper left window. The portion is selected using the cursors.

c. The upper right hand window is the IV curve for the capacitor

Is the current a linear function of the voltage across the resistor? Is the current a linear function of the voltage across the capacitor? Immediately before the square wave voltage changes from +5 V to -5 V, what is the current flowing in the circuit, and what are the voltages across the resistor and the capacitor? Immediately after the square wave switches, what is the current flowing in the circuit, and what are the voltages across the resistor and the capacitor? Is the absolute magnitude of either of the voltages larger than 5V? Is the voltage linear on a semi-log scale? What is the decay rate for the resistor voltage, and is it consistent with what you would expect? The white box at the right of the window shows the time points that are averaged to make the plot. Choose 1 and take data. Choose 10 and take data again. Did the signal change? If so, how? The signal to noise improves if the averaging number increased, but if you make it too large the data becomes distorted. Why?

Bonus: Add the second 0.1 microFarad capacitor in parallel with the original 0.1 microFarad capacitor. Draw a schematic of this circuit. Repeat the voltage vs time measurement. Is the new RC time constant what you would predict? Explain. Look at the time dependence of the resistor voltage when the resistor is in series with a series combination of the two 0.1 microFarad capacitors. Draw a schematic of this circuit. Repeat the voltage vs time measurement. Is the new RC time constant what you would predict? Explain. Bonus: Compare with the case where the 1 k Ohm resistor and the 10 k Ohm resistor are in series with the 0.1 microFarad capacitor. Draw a schematic of this circuit. Repeat the voltage vs time measurement. Is the new RC time constant what you would predict? Explain. Consider the case where the 1 k Ohm resistor and the 10 k Ohm resistor are in parallel with each other and the parallel combination is in series with the 0.1 microFarad capacitor. For both cases draw a schematic of this circuit. For both cases, repeat the voltage vs time measurement. Is the new RC time constant what you would predict? Explain. What does the result of these last to measurements suggest about making approximations in circuit diagrams to simplify analysis before applying Kirchoff’s Laws? Bonus: change the frequency of the square wave from 1 Hz to 1 MHz. Over what frequency range is the RC response to the square wave effectively a response to a DC voltage? Bonus: Look at the voltage for a parallel combination of the 0.1 microFarad capacitor and the 100 Ohm resistor where the parallel combination is in series with the 1 kOhm resistor. Look at the voltage for a parallel combination of the 0.1 microFarad capacitor and the 100 Ohm resistor without an additional resistor in series. Double Bonus: Look at the IV relationship for the capacitor when the circuit is driven by a sine wave. Triple Bonus: Measure the IV using Loggerpro and explain why it produces the wrong voltage responses.

Challenge Problems:

1. Design a voltage rectifier that takes an AC input and converts it to an output that contains only positive voltages. Such a device is called a half wave rectifier. Use 4 diodes, a resistor, and a capacitor to construct a full wave rectifier that takes an AC input and produces an output voltage that is approximately equal to the absolute value of the input voltage.

2. Design a voltage doubler or tripler that starts with a 60 Hz 5V signal from the signal generator.

3. Use a combination of diodes and capacitors to create a DC voltage larger than the peak AC voltage.

4. Design a clock/timer using a comparator 5. Send and receive an optical Morse Code SOS transferred over the longest distance 6. Measure the IV curve for a transistor as a function of gate voltage for a NPN

transistor. Also, plot collector current as a function of base current. The ratio is called beta. The figure below shows the symbols for both npn and pnp resistors, as well as a schematic showing the physical connections to the 3904 npn. The figure at the right is a circuit hint. Explain your result and predict the result for a PNP transistor. Check your prediction. Bonus: Change the base resistor to 10k and try again. Design a voltage amplifier. Observe change when the transistor is cooled to liquid nitrogen temperatures or heated with a hair dryer.

7. Theory Challenge: In the lab you considered the IV relationships for three devices

and their departures from simple Ohmic predictions. Though Chapter 1 of Purcell mentions that charge is quantized, this fact is ignored in most of 15b; however, it does play an important role in nanoscale devices. An example is the Coulomb blockade. It can be described theoretically as two conductors separated by a small non-conducting gap. Classical mechanics predicts that no charge can flow across the device, but quantum mechanics allows charge to tunnel from one side to the other. The quantum mechanics predicts that the tunneling current should be proportional to the voltage, that is it should follow Ohm’s law; however, a small gap between conductors is also a capacitor. If the two conductors are initially uncharged, the current due to the applied voltage will begin to build up a charge on the plates. What is the potential change due to each particle with charge e that tunnels across the gap? Does this increase or decrease the potential applied by the voltage source? Sketch the IV curve for this device when the tunneling current is taken into account. How could this effect be used to make a quantum transistor? What dimensions would be required for one single electron to control the charge flow at room temperature?

Supplemental Information Breadboards Breadboards are used to quickly create model circuits without creating the mass of wires that would be required to connect everything with alligator clips or micrograbbers. An image of a breadboard is shown on the left below. They consist of a series of holes into which the leads from circuit elements can be inserted. Leads are the wires that stick out of circuit elements and allow them to be connected. The holes are connected on the back of the breadboard as shown in the diagram on the right below, where the light blue lines indicate holes that are electrically connected. The holes between the red and blue ones at the top and the bottom of the breadboard are connected horizontally. They are usually used to distribute the voltage from the power supply to the circuit. The two central regions are electrically connected in columns. They are used to connect circuit elements to each other. The photograph in the center below shows the back of the breadboard with part of the protective insulation peeled off. The metal strips that connect the central columns and the edge rows are clearly visible.

An image of a circuit and the equivalent schematic are shown below as an example.

Spectrometer Use Instructions Use a USB cable to connect the Vernier Spectrometer to the computer. (Note: Do not connect the spectrometer to a USB hub.) The Spectrometer is powered by your computer through the USB cable. 2. Start the Logger Pro 3.4.5 software. 3. Select Connect Interface → Spectrometer → Scan for Spectrometers from the Experiment menu. 4. To calibrate the Spectrometer, choose Calibrate → Spectrometer from the Experiment menu. The calibration dialog box will display the message: “Waiting …seconds for lamp to warm up.” (see Figure 1) The minimum warm up time is one minute. NOTE: For best results, allow the spectrometer to warm up for at least three minutes. Follow the instructions in the dialog box to complete the calibration. Click OK. Figure

5. Choose Change Units → Spectrometer → Intensity from the Experiment menu. Intensity is a relative measure. 6. Aim hole in the spectrometer at the light source. Click . Observe the graph of intensity vs. wavelength. Click to end data collection. Note: If the spectrum maxes out with flat tops to peaks, reduce the integration time. The screen will then display intensity as a function of wavelength, where the graph is overlayed on a rainbow that displays the color corresponding to that wavelength.

Symmetries in Physics In the discussion above, we compared the IV curves for a positive voltage across a device and compared that to the result for a negative voltage. If the device is uniform, then the ratio of I to V for the two systems should be identical. If the device has different properties at one end than at the other, then the two results may not be identical. This system is essentially one dimensional; therefore, if the device is invariant under translation along the current carrying direction (shown in the figure below as the device having the same purple property everywhere), it is also invariant under reflection about its center. In this case, the result of all four physical measurements shown must be exactly the same. In contrast, if the device has two different sides with different properties, then it is not invariant under translation or reflection. Such a device is shown below with red and blue sides where the two sides have physically distinct properties. Measurements where one sets up two sets of experiments that should be identical if a symmetry exists, but may yield different results if the symmetry does not exist have and continue to play a vital role in our understanding of the basic properties of the universe. http://www-project.slac.stanford.edu/e158/parityviolation.html http://ccreweb.org/documents/parity/parity.html

Symmetry is one of the most important concepts in physics. Emily Noether showed that conservation laws in physics are linked symmetries in the mathematical formulation. Conservation of energy, momentum, and angular momentum are associated with invariance as a function of translation in time, position, and angle respectively. There are many other more subtle symmetries in physics. Until 1957, inversion, or mirror, symmetry was expected of nature. It came as some surprise that parity, P, symmetry is broken by the radioactive decay beta decay: electrons from the beta decay are preferentially emitted in the direction opposite that of the aligned angular momentum of the nucleus process a discovery made by C.S. Wu and her collaborators. When it is possible to distinguish these two cases in a mirror, parity is not conserved. As a result, the world we live in is distinguishable from its mirror image. At present there is no proof that the combination of CPT (charge,parity, and time) is not conserved, that is the universe looks the same if CPT are ALL reversed. Evidence for CPT symmetry violations are eagerly sought http://www.physics.indiana.edu/~kostelec/faq.html http://www.atomic.princeton.edu/romalis/CPT

Great care must be taken to determine that observed changes are due to variables controlled by the experimentalist. Sometimes experimental conditions that are assumed to be identical are not because some important variable has been ignored. For example, Jerry Gabrielse research group at Harvard suddenly got different results when the subway connection from Harvard Square to Alewife opened. They were still doing exactly the same experiments, but the magnetic fields associated with the running of the subway changed the conditions in their lab. Sometimes, the phase of the moon even matters. http://news-service.stanford.edu/news/2000/march29/linac-329.html http://accelconf.web.cern.ch/accelconf/e00/PAPERS/MOP5A04.pdf

http://www.agu.org/pubs/crossref/2003.../2001JB000569.shtml A crucial aspect of experimental physics is sorting out what factors determine the outcome of your experiment.

Resistor Color Code

Additional Capacitor Information In this lab you are using ceramic capacitors. You used electrolytic capacitors in the previous lab. Ceramic capacitors typically have smaller capacitance, but are more ideal than electrolytic capacitors: electrolytic capacitors leak more and show inductive behavior at high frequencies. Also, unlike electrolytic capacitors, ceramic capacitors are not polar. Voltage and capacitance ranges for different types of capacitors are shown below, and additional discussion of capacitor types and applications is available.

http://www.electrosuisse.ch/display.cfm?id=113982

Diodes In a vacuum diode, the motion of the charges is particularly simple since there are no collisions, as discussed in section 4.2. Vacuum diodes are still used in some specialty applications such as ion gauges where the very rare collisions between ions allow low pressures to be measured ; however, in most cases they have been replaced by semi-conductor diodes consisting of a P doped semi-conductor (positive free carriers) adjacent to an N doped semiconductor (negative free charge carriers). An excellent applet shows the current to voltage relationship for a diode . Semiconductors are discussed in section 4.9 of Purcell.

Photodiodes

Photodiodes produces a current that is proportional to the light intensity hitting the diode, so when a voltmeter is connected to its leads, the current will flow through the resistor in the voltmeter resulting in a voltage difference that appears at the voltmeter output. A photodiode is basically an LED operating in reverse: the internal electric field of a PN junction is used to separate an electron hole pair created by a photon hitting the diode. The same principle is used in solar cells to generate electricity from sunlight

US Electrical Power Distribution System

The power generated by power stations has voltage that changes periodically as a function of time. In the United States at a wall outlet, the voltage as a function of time is approximately V = 170 Sin (2 π 60 t) a sine wave with a frequency of 60 cycles/second with a root mean square(RMS) voltage of 120 V, corresponding to an amplitude of 170 V and a peak to peak excursion of 340 V. The root means square value of an AC voltage is equal to the amplitude of the voltage divided by the square root of 2. AC has at least three advantages over DC in a power distribution grid:

1. Large electrical generators generate AC naturally, so conversion to DC would involve an extra step.

2. Transformers can either increase or decrease the voltage. In power supply systems a chain of transformers changes the voltage in steps from 155,000 to 765,000 V at the power plant to 110 V at the wall plug. Transformers must have alternating current to operate

3. It is easy to convert AC to DC but expensive to convert DC to AC, so if you were going to pick one or the other AC would be the better choice.

Electrical Power Delivery in the US All power companies use an alternating current transmission scheme with long range transmission voltages sometimes in excess of 100,000 volts, with long distance transmission at voltages from 155,000 to 765,000. The Three wires leave the power station, where there is a phase delay of 120 degrees between each of the three wires, as shown below. V1=Vo sin[ 2π 60t] V2=Vo sin[ 2π 60t -2 π/3] V3=Vo sin[ 2π 60t -4 π/3]

Three phase systems are frequently used in to power large electric motors, but most residences get only 1 phase power. Local Distribution Power is brought down from the high voltage transmission towers to substation transformers. Substation transformers lower the voltage for local distribution via power poles. The power pole

line can come all the way to your home or be converted to an underground distribution system for the final leg to your house. Only one phase is required for residential applications, so at some point there is a tap that attaches to only one of the three phases. Another transformer steps the one phase voltage down to the two 120 volt circuits, plus a neutral wire, to your house. A photo of a typical pole transformer that converts 7200V to 120V is shown below, with an electrical schematic of the transformer shown at right. Some systems now use14,400 V instead of 7200. Transformers are treated in Purcell in Chapter 7. New federal regulations require that the energy efficiency of pole transformers increase by 2010. One increased efficiency is provided by changing from changing the internal wiring form Aluminum to Copper because copper has a higher conductivity.

The one phase voltage is shown at the top of the pole, with the ground wire even with the top of the transformer. The 7200 V is the difference between the one phase voltage and the ground. This is fed into one side of a transformer. The other side is a center tap transformer with three outputs. The three output wires leave the transformer and enter your house, as shown in the diagram on the right above. The voltages as a function of time are shown below for a total time interval of 0.1 seconds. The blue corresponds to the far left wire, the green corresponds to the central wire, and the red corresponds to the far right wire. The red and the blue are 180 degrees out of phase, so the three voltages are Vblue =170 sin[ 2π 60t] , Vgreen =0 , V red=170 sin[ 2π 60t+π]

Notice that the green is the sum the red and the blue. Most residential power applications use a connection between one of the hot wires (either red or blue) and the green wire. This gives

110 V RMS 60 cycle power. Some appliances, such as electric dryers use 240 V RMS. This is obtained by using the difference between the hot wires, shown by the purple line below, where the other lines are the same as those shown above.

. Power Meter The power meter measures the power entering your house. A photo of a typical power meter is shown above. The power meter is in line with the power feed from your nearest transformer. The Watt is the unit of electrical energy. One kiloWatt-hour is equivalent to the use of 1000 Watts of electricity (ten 100-Wattbulbs) for one hour. A kiloWatt-hour varies with location. Hawii is the most expensive at 21.48 cents/kW-hour. Massachusetts is third most expensive at 15.13 cents. Idaho is cheapest at 4.91 cents. The US average is 8.77 cents. http://www.eia.doe.gov/fuelelectric.html A nice map of price by state is given at http://www.eia.doe.gov/fuelelectric.html Load Centers A load center is positioned between a breaker box and the power meter. They are located near the power meter and therefore are frequently found in your garage. The load center has one big breaker for each of the 120 volt circuits from the power meter. A typical main breaker in a load center is 150 amperes (amps) Breaker Boxes The diagram below shows the pole transformer picture above producing the two 120 V AC signals plus the neutral voltage, where the red, light green, and blue correspond to the colors in the voltage plots above. The dark green shows the connection to the ground. The neutral and the ground are attached at the breaker box, so they represent the same voltage.

The red and blue power feeds are connected to two power buses located behind the circuit breakers. The upper breaker highlighted in blue corresponds to a 110V circuit. The black wire that comes down from the breaker corresponds to the black wire shown at the bottom in the three wire set that goes out to the wall outlet. The white wire going to the wall outlet is attached to the neutral, and the beige wire is attached to the ground. The lower left hand breakers in the diagram above (pink 30-amp ganged breakers) correspond to the 240 V circuit that goes out to the dryer in the picture above. The top breaker in this pair, with the black wire leading to it, is connected to one 120 volt bus attached to the blue wire shown coming into the top of the box from the pole transformer. The bottom breaker in this pair, with the red wire leading to it, is connected to the other 120 volt bus that is attached to the red wire coming from the pole transformer into the box. The white wire is connected to the neutral, and beige wire is connected to the ground. The difference of voltages on the red and black wires is 220V rms. The difference between the black and the white is 110V RMS, as is the difference between the red and the white. House Wiring Now let's take a look at the wall outlet circuit that starts with the black wire leading down from the top left 20-amp breaker in the breaker box image above. This is a single 120 volt circuit that will service 2 or 3 wall outlets. If we follow this wall outlet circuit out to a duplex wall outlet, it will be wired as follows:

http:// www.cornerhardware.com/howto/images/ht052_1.jpg Note that the vertical slot to the left is longer than the one to the right, to distinguish the hot wire from the neutral wire. If the outlet is wired properly, the white wire is connected to the longer neutral slot to the left and the hot black wire is connected to the short slot to the right. The semicircular connection below the slots is connected directly to the ground outside the house. It is not connected to the neutral except at the breaker box. The wiring for a 220V four plug receptacle is shown at right. Again, the semicircular slot corresponds to ground. In this case, BOTH of the side slots are hot and connected to the two out of phase 110V bus bars, so the difference between them is 220V. The lower L shaped connector is the neutral. The outer case of an appliance should always connected to the safety ground, so it doesn't make much difference what happens to the other wires. If the neutral wire shorts to the case nothing happens. If a hot

wire shorts to the case, a short circuit is presented to the breaker and it should open. The safety ground prevents YOU from being the path for a circuit from a hot wire shorted to the case to ground. Much of the information and many of the pictures in this document were adapted from http://www.the-appliance-clinic.com/electwiring.html and http://science.howstuffworks.com/power.htm/printable

Electricity Generation and Distribution to the Local Network

The physics underlying electrical power generation is covered in Chapter 7 of Purcell, but the material below gives an overview of the energy sources that are used to produce electrical power, and the physical infrastructure used to transfer the power from the power stations to users. The discussion above began with the long distance transmission lines, but there are two earlier stages : the generation of the power at the power plant and the increase in voltage that occurs before the long distance transfer begins. All the steps are shown below in a diagram from How Stuff Works, where I have added the voltage levels that are typical at each stage. The second image below is from Encarta. It shows the actual values of different long haul distribution lines, as well as showing the few High Voltage Direct Current lines that now exist. High voltage direct current is becoming more attractive for reasons including: improved electronics allow better conversion between AC and DC; the feasibility of linking AC power grids whose phases are not synchronized; reduced losses in comparison to AC in very long haul applications where the capacitance of the wires becomes important; http://en.wikipedia.org/wiki/High-voltage_direct_current

It may at first seem odd that such high voltages are used for power transmission, and that there is an effort to keep increasing the voltages not only for long distance transmission, but also for transmission from power substations to pole transformers. The answer is that increasing the voltage reduces the energy lost as the power is transmitted. Transmitting electricity at high voltage reduces the fraction of energy lost to heating. Consider an electrical power delivery system that must deliver a power P=IV where I is the current and V is the voltage. Let a metal power line be characterized by a resistance R. (In chapter 8 of Purcell complex reactance will be introduced, allowing one to include AC signal losses due to the capacitance of the cable, but the basic scaling laws of power efficiency vs voltage are the same). The energy lost in the transmission line is then I2R=(P/V)2 R. Thus the power loss decreases inversely with the square of the voltage and proportional to the resistance, driving one to try to increase energy efficiency by increasing line voltage. This process cannot go on without limit, At voltages larger than 2,000 kV corona discharge losses are so large that they can offset the lower resistance loss in the line conductors. A nice video of a corona discharge is available. Transmission and distribution losses in the USA were estimated at 7.2% in 1995 , and in the UK at 7.4% in 1998.

As discussed above, low electrical resistance in cables can also improve energy efficiency; however, the installation and maintenance costs have favored higher conductivity materials. Thus aluminum is often used in transmission lines, though its conductivity is small than copper because its cost is lower as is its conductivity to weight ratio The issue of long term energy efficiency due to improved conductivity vs short term installation cost is a significant issue, not only for long distance power transmission, but also for local energy use. As noted above, new pole transformers are required to use Cu rather than Al to improve efficiency. In the1970’s houses were wired with Al wire rather than Cu wire to save money in new construction. Unfortunately, there are many safety problems associated with Al wiring, and the practice has been discontinued.

In order to produce electrical power, the power station must consume another form of energy. In the US this is dominantly the burning of hydrocarbons, dominated by coal. A diagram of the primary energy sources for US power plants are shown in the map below from the US department of energy. Once the power is generated, it needs to be distributed. Power distribution in the US is divided into regional authorities, some of which include Canada and Mexico. The regional power authorities are shown in the pack at right, which also shows the power control centers and connections that are used to redistribute power around the US to provide continuous power despite changes in supply and demand.

http://www.nerc.com/regional/NERC_Regions_BA.jpg

A grid works very well as a power distribution system because it allows a lot of sharing. If a power company needs to take a power plant or a transmission tower off line for maintenance, the other parts of the grid can pick up the slack.

The thing that is so amazing about the power grid is that it cannot store any power anywhere in the system. At any moment, you have millions of customers consuming megawatts of power. At that same moment you have dozens of power plants producing exactly the right amount of power to satisfy all of that demand. And you have all the transmission and distribution lines sending the power from the power plants to the consumers.

This system works great, and it can be highly reliable for years at a time. However, there can be times, particularly when there is high demand, that the interconnected nature of the grid makes the entire system vulnerable to collapse. Here's how that happens:

Let's say that the grid is running pretty close to its maximum capacity. Something causes a power plant to suddenly trip off line. The "something" might be anything from a serious lightning strike to a bearing failure and subsequent fire in a generator. When that plant disconnects from the grid, the other plants connected to it have to spin up to meet the demand. If they are all near their maximum capacity, then they cannot handle the extra load. To prevent themselves from overloading and failing, they will disconnect from the grid as well. That only makes the problem worse, and dozens of plants eventually disconnect. That leaves millions of people without power.

The same thing can happen if a big transmission line fails. In 1996 there was a major blackout in the western U.S. and Canada because the wires of a major transmission line sagged into some trees and shorted out. When that transmission line failed, all of its load shifted to neighboring transmission lines. They then overloaded and failed, and the overload cascaded through the grid.

In nearly every major blackout, the situation is the same. One piece of the system fails, then the pieces near it cannot handle the increased load caused by the failure, so they fail. The multiple failures make the problem worse and worse and a large area ends up in the dark. One solution to the problem would be to build significant amounts of excess capacity -- extra power plants, extra transmission lines, etc. By having extra capacity, it would be able to pick up the load at the moment that something else failed. That approach would work, but it would increase our power bills.

http://people.howstuffworks.com/blackout.htm http://www.aip.org/tip/INPHFA/vol-9/iss-5/p8.html The blackout provided an opportunity to measure the pollutants emitted by powerplants since there was no emission during the blackout. The reduction in emissions was both rapid and significant. Electrical power is only one component of our energy use. The chart below shows the original sources for US energy, the final form in which it is used is shown below. Notice that almost 60% of the energy is actually lost.

Physics 15b Lab 2: Current, Ohm's Law, Resistance, EMF

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