Physics 15b PSI Week 3: Current, Resistance, Ohm’s Law

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 V0 > 0 differs from its response to –V0 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.

Pre-lab Questions: 1. Ohm’s Law: Consider an ohmic system driven by an alternating voltage

V t( ) = V0 cos !t( ) . Plot V as a function of time for t between from 0 to 4! /" . Plot I as a function of time for t between from 0 to 4! /" . 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).

2. Resistance of a metal as a function of temperature: 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? 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?

3. For a voltage as a function of time given by V t( ) = 170 V( )cos 2! 60 Hz( )t( ) , what is the RMS (root mean square) 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

2 / R .

Bonus Question:

Assume that you want to measure the current I that flows in a device as a function of the voltage V 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 = !R2 and R3 =R2!

, where ! and ! are both << 1. Show that to first order in ! and

! , the ratio of the measured I/V ( I1 /V3 ) to the true IV ( I2 /V2 ) is 1+ ! , independent of ! .

Short Summary of How Diodes Work

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.

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 http://www.utc.edu/Faculty/Tatiana-Allen/ivcurve.html

Lab Handout

Lab Outline A. Relationships between Voltage, Current, and Resistance

a. 150 Ohm Resistor b. Light Bulb c. LED

B. What comes out of the wall? a. Measured using a voltmeter b. Measured using an oscilloscope

C. Challenge a. How can you turn an AC voltage source into a DC voltage source?

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 charge propagation in semi-conducting materials, including diodes formed by combining an n-type semiconductor with a p-type semiconductor.

3. Study parity detection and hysteresis in simple systems 4. Learn how to assemble temporary circuits 5. Discover some effects of apparatus choice on data acquisition and measurement 6. Study effects of combining resistors, diodes, and capacitors 7. Practice with the correspondence between circuit schematics and actual circuits 8. Learn about the form in which electrical power is distributed in the United States

Useful Information

Circuit schematics will be used extensively in this lab, so a table of circuit symbols is provided below.

Physics 15b PSI Week 3: Current, Resistance, Ohm’s Law 1. Relationships between Voltage, Current, and Resistance

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.

Materials: 150 Ohm resistor; light bulb; LED; BNC T; BNC to micrograbber; function generator; Vernier differential voltage probe; Vernier current probe; oscilloscope 1. 150 Ohm Resistor Objective: 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 and Measurement Directions 1. Setup the scope to monitor the signal generator

a. Connect the BNC T to the output of the signal generator 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

3. Connect the circuit as shown above

a. From the BNC T on the signal generator, take a BNC cable and a BNC-to-micrograbber connector and use it to supply power to the breadboard.

b. Connect the leads of the differential voltage probe across the resistor, as shown. Rather than clipping the alligators on the probe directly to the resistor, use a short jumper wire on each alligator and stick the free end of the jumper into an appropriate hole on the breadboard.

c. Connect the current probe in series with the resistor, as shown, with the black end connected to ground (black) of the power supply.

4. Setup Logger Pro to acquire data a. Make sure that the LabPro Box is connected to the USB input on the computer. b. Open IV_Template.cmbl. This is a LoggerPro file that will assist you in taking

data. This program should be in the week4 folder on the desktop, but if it is not, you can download it from the 15b website. A screen shot of the program is shown below. There are three graphs: voltage vs time, current vs time, and current vs voltage.

5. Begin data acquisition 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, click on the graph

and then click autoscale from the toolbar. If LoggerPro makes bad choices using autoscale, rescale the plot manually.

ii. If the current is not appearing or the voltage across the resistor is not appearing, please ask for assistance.

Is the resistor ohmic? Explain. Calculate the effective resistance as a function of voltage. Hint: Try a linear fit on the IV curve. What does it tell you? How does the measured resistance compare with the nominal resistance? Is the device symmetric? Is it hysteretic? Explain. 7. Repeat data at 0.2 Hz Note: you would get the same results for a 20 Hz sine wave. Bonus: Repeat with a 20 Hz sine wave. Bonus: Repeat with a 2 Hz sine wave. Bonus: Repeat with a 20 Hz square wave. 2. Light Bulb

Objective: Measure the IV (current to voltage) curve for a light bulb using the function generator as a voltage source for a voltage range of +-5V. Apparatus Assembly Directions 1. Keep the same setup you already have, but replace the 150! resistor

in your circuit with the light bulb. Do not attach any alligator clips directly to the leads on the bulb, which are fragile; use jumper wires and the breadboard instead.

2. Tune the signal generator to 0.2 Hz and begin data acquisition

Is the light bulb ohmic? Is it symmetric? Is it hysteretic? How many light pulses does the light bulb emit during one voltage cycle? Estimate the resistances of the bulb at different times during one voltage cycle. 3. Change the signal generator frequency to 20 Hz by pressing the 100 Hz

frequency selection button (don’t adjust the knobs themselves). Repeat the measurement.

Explain any differences between the 20 Hz measurement and the 0.2 Hz measurement. What is the implication of this result for the question from week 2, where you measured the frequency at which your eye no longer saw the light bulb flashed?

3. LED Apparatus Assembly Directions 1. Keep the same setup you already have, but replace the light bulb in your circuit

with an LED. Again, do not attach any alligator clips directly to the leads on the LED; use jumper wires and the breadboard instead.

a. The LED has relatively short “legs”, so you might need to rearrange your circuit slightly on the breadboard to accommodate it.

b. The LED is directional, so make sure you know which way you are putting it into your circuit.

c. The longer “leg” is the + end; the flattened side is the – end. The LED will

light up when current is flowing through it in the direction from + to –. 2. Tune the signal generator to the 0.2 Hz and begin data acquisition Is the LED ohmic? Is it symmetric? Is it hysteretic? What is the voltage across the LED when it begins emitting light? What is the current through the LED when it begins emitting light? How many light pulses does the LED emit during one voltage cycle? Explain your result. 3. Look at the signal generator output using the oscilloscope (by connecting a BNC

to the free end of the BNC T junction). Observe what happens to the scope reading when you disconnect the other BNC (the one that powers the breadboard).

Does the signal generator output change when you disconnect the circuit? Why? 4. Repeat the measurement with a 20 Hz triangle wave. Explain any differences between the 20 Hz measurement and the 0.2 Hz measurement.

5. Use the LED to determine the frequency at which your eye no longer detects

flashing. Explain why the result is different form the light bulb case. 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. B. What comes out of the wall? Goal: Learn about the form in which electrical power is delivered to consumers in the US. Materials: light source box; multimeter; scope probe; scope; BNC cables Objective: Measure the AC voltage at a wall outlet 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. A detailed discussion of power generation and delivery in the US is given in a supplemental information section.

The picture above shows the three connections at a typical wall outlet. For safety, instead of sticking probes directly into an outlet, we will use a lightbox which makes the connections safely accessible.

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. Use the AC voltmeter to measure the voltage coming out

of the wall a. Set the multimeter to measure AC voltage (“V~” icon) b. Put the multimeter red and black probes into the red

and black holes shown in the diagram on the left above.

c. Turn on the lightbox. 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: Repeat the experiment on the DC voltage setting (“V=” icon). Explain your answer. 2. 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 b. Monitor the voltage difference between neutral and ground on Ch2

Channel 1 shows the difference between hot and ground. How well is CH1 described by V = 170 Sin (2 " 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?

C. Challenge Goal: Turn an AC voltage source into a DC voltage source. Using your signal generator (or the wall outlet), you can produce an alternating (AC) voltage source. Many devices require a steady (DC) power supply. How do you turn one into the other? This exercise will help you to begin thinking about such issues. Consider the following input voltage (square wave, 6 V amplitude, 5 Hz frequency):

Challenge 1: Design and build a circuit that will take that input voltage and create an output voltage (e.g. the voltage across some resistor in the circuit) that looks like this:

In words, the output voltage never goes negative; it is either the positive half of the wave only, or zero. You may use any combination of resistors and diodes; it’s okay if the maximum output voltage is a bit less than the maximum input voltage. When you get this working, show it to an instructor. Challenge 2: Design and build a circuit that will take that same input voltage and create an output voltage (e.g. the voltage across some resistor in the circuit) that looks like this:

In words, the output voltage is essentially the absolute value of the input voltage (perhaps with a slightly smaller amplitude). Again, you may use any combination of resistors and diodes. When you get this working, show it to an instructor. Try your circuit using a sine wave input. What does the output look like? Later in the semester, we’ll learn how to smooth out the output from challenge 2 into a steady DC voltage.

End of the Required Experiments

Supplemental Information 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 t( ) = 170 V( )sin 2! 60 Hz( )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-mean-square value of an AC voltage is equal to the amplitude of the voltage divided by 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[2" 6 0t] V2=Vo sin[2" 6 0t – 2" /3] V3=Vo sin[2" 6 0t – 4" /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[ 2" 60t] , Vgreen = 0 , V red = 170 sin[ 2" 60t + "]

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 reason 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 the 1970s, 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, when 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.