Physics 222 Ohm's Law Lab Report
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Transcript of Physics 222 Ohm's Law Lab Report
Name: Emily A. Gatlin Partner: Whitney Heaston
Performed: January 21st, 2009 & January 28th, 2009 Date: 4 February 2009
Class: Physics 221, Section 004 T.A.: John Carruth
OHM’S LAW
1 | Page
INTRODUCTION
The first part of the experiment uses the concept of elementary direct circuits to help
demonstrate Ohm’s law. First, it is critical to understand how to read schematic diagrams. The three
most important symbols (shown below):
Power Supply Bulb Switch
Ohm’s Law is the relationship between the current flowing through resistance, R and the potential
drop across it . Ohm’s Law states the voltage or electric potential in direction proportional to the
product of the current and the resistance where current is in Amps (A), voltage in volts (v), and
resistance in Ohms (Ω). Therefore, the relationship:
expresses Ohm’s law (shown below).
Using this concept, part I of the experiment demonstrates the basics behind DC circuits both in the
configurations of simple series and parallel circuits. Using these simple elements, the experiment
develops enough of the conceptual understanding of DC circuits to make predictions about the
variations presents among different circuits.
+ ―
Ohm’s Law Parts I & II Emily A. Gatlin
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In addition, part I of the experiment shows the basic model behind how electrical components
consume power. Power is the rate of performing work and electrical power is the amount of
electrical energy expanded per unit time.
The conceptual understanding of power derives from the relationships described in Ohm’s Law.
Since, work or mechanical energy is the product between the electrical charge times a
potential difference ( ― . The use of the relationships defined in Ohm’s law offers a
measurable solution to calculate work of an electrical system by plugging in the power equation.
Clearly, the manipulation from Ohm’s law behind voltage, current and resistance allows the easy
calculation of power. Thus, the first part of the experiment clearly demonstrates Ohm’s Law using
the mastery measuring voltage and current in both series and parallel to calculate the total
resistance of a system.
The second part of the experiment also uses Ohm’s Law to demonstrate the relationship
between voltage, current and resistance in both series and parallel configurations. In addition, this
portion of the experiment focuses more in-depth on the use of ammeters, voltmeters, ohmmeters,
and multimeters to gather the data for voltages, currents, and resistances. This part of the
experiment emphasizes the total resistance present within a system and shows how this relationship
varies depending on the configuration. Therefore, this part of the experiment highlights the
importance behind the relationship of the resistance when in parallel. Most houses utilize this
Ohm’s Law Parts I & II Emily A. Gatlin
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relationship because as more resistors add to the circuit, the total resistance of the circuit decreases
until the source cannot supply enough.
Ohm’s Law shows resistance is . In a closed circuit with the resistors in a series has a current
supplied by the battery or electromagnetic force (εmf) supplier flow through each resistor. In this
arrangement, current is constant. However, the voltage is the sum of the individual voltages across
the circuit and the resistance is the sum of individual resistors throughout the circuit.
→
→
Resistors in parallel have one end of each resistor connected to a common point and each of the
other ends connected to another common point. The current is divided among the three resistors
where the current rejoins into a common current IT flowing back to the battery or power source. In a
parallel arrangement, the following relationships exist
PROCEDURE
PART I
Ohm’s Law Parts I & II Emily A. Gatlin
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For the first experiment, the apparatus used consisted of a prototype circuit boards with
banana jacks for wiring the circuits, a Pasco® model PI-9877 power supply, stackable banana plugs
with light bulbs or jumper wires, banana plugs with switches and leads with banana plugs.
The first section of the experiment tested had a simple circuit with one light bulb in the circuit. The
voltage was systematically increased and the respective current reading was recorded. Power usage
calculated using the voltage and current readings obtained.
The second section had two light bulbs arranged in a series circuit with the voltage controlled
and systematically increased while recording the current simultaneously. Power was calculated for
the two light bulbs.
The third section had the light bulbs arranged in parallel circuit. Again, the voltage was
decreased systematically and the current recorded. The power consumed by the two bulbs was
calculated using this data.
The fourth section had two light bulbs in series with one another and in parallel with the third
light bulb. The same systematic decrease of voltage was controlled with the recording of the
respective current reading. Again, the power consumption was calculated using the obtained data.
In the fifth section, the two light bulbs were in parallel with each other that were in series
with a third one. In this section, predictions regarding the nature of the power usage were made
while the voltage was systematically decreased with the current reading for each decrease was
recorded.
Ohm’s Law Parts I & II Emily A. Gatlin
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In the sixth section, a switch was added to the light bulb in parallel to the series and
predictions were made regarding how the switch’s position would affect the circuit activity on the
light bulb.
PART II
In the second part of the experiment, the apparatus consisted of two Meterman Model 15XP
digital multimeters (DMMs), a prototype circuit board with banana jacks, a Pasco® PI-9877 power
supply, stackable banana plugs, and assorted leads with banana plugs.
First, the effect of the ohmmeter was assessed. The apparatus was set up in the above
configuration. The Meterman 15XP was used to measure resistance as the ohmmeter. Using the
color bands on the resistors that give the values of resistance are compared to the measure values by
the ohmmeter.
Next, the single resistor is arranged with the anameter in the series with the resistor and the
voltmeter in parallel to the resistor. The values for current were measured as the voltage was
increased from zero to 18 volts. These values were used in the calculation from the graph of voltage
versus current to determine the resistance.
For the resistors in parallel, the ohmmeter was also in parallel with the resistors in order to
obtain the measured value for the resistors in parallel. However, the calculated value was obtained
with the anameter in a series with R3 and the voltage meter parallel to the power source (see
diagram). The voltage was again incremented by 1-volt from zero to 18-volts while the current and
voltage was measured. This data was added to the graph created in the previous step with the single
resistor.
Ohm’s Law Parts I & II Emily A. Gatlin
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In the resistors in series, the ohmmeter was placed in series with the resistors to obtain the
measured value initially. Then, the steps for the single resistor and resistors in parallel was repeated
to find the effect of the resistors in this configuration. Lastly, the voltage readings were verified by
moving the voltmeter to be in parallel to each of the three resistors and the data was recorded.
DATA
EXPERIMENT PART I VOLTAGE (V) CURRENT (I) POWER (P=IV) RESISTANCE
0 0 0 0
1 0.03 0.03 33.33333333
2 0.044 0.088 45.45454545
3 0.054 0.162 55.55555556
4 0.062 0.248 64.51612903
5 0.072 0.36 69.44444444
6 0.078 0.468 76.92307692
7 0.082 0.574 85.36585366
8 0.09 0.72 88.88888889
9 0.098 0.882 91.83673469
10 0.104 1.04 96.15384615
11 0.112 1.232 98.21428571
12 0.116 1.392 103.4482759
13 0.124 1.612 104.8387097
14 0.126 1.764 111.1111111
15 0.134 2.01 111.9402985
16 0.14 2.24 114.2857143
17 0.144 2.448 118.0555556
18 0.15 2.7 120
PART II
VOLTAGE CURRENT POWER RESISTANCE
18 0.098 1.764 W 183.6734694
BULB 1
18 0.098 1.764
PART III
VOLTAGE CURRENT POWER RESISTANCE
Ohm’s Law Parts I & II Emily A. Gatlin
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18 0.292 5.256 61.64383562
BULB 1
9 0.292 2.628
BULB 2
9 0.292 2.628
PART IV
VOLTAGE CURRENT POWER RESISTANCE
18 0.246 6.642 109.7560976
BULB 1
9 0.246 2.214
BULB 2
9 0.246 2.214
BULB 3
9 0.246 2.214
PART V
VOLTAGE CURRENT POWER RESISTANCE
18 0.128 2.304 140.625
BULB 1
4.5 0.128 0.576 35.15625
BULB 2
4.5 0.128 0.576 35.15625
BULB 3
9 0.128 1.152 70.3125
EXPERIMENT PART II
RESISTORS IN PARALLEL
y = 132.71x - 3.2932
-5
0
5
10
15
20
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
V
o
l
t
a
g
e
Current
Voltage Vs. Current
Ohm’s Law Parts I & II Emily A. Gatlin
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Band #1
Value Band #2 Value Band #3
Value Band #4 Value Tolerance
Resistor #1
Br 1 Red 5 Red 2 Silver 1500 10%
Resistor #2
Br 1 Black 0 Red 2 Silver 1000 10%
Resistor #3
Br 1 Green 5 Red 2 Gold 1500 5%
Measured Values Slope Values %Difference Inverse Slopes and Sums
Resistor #1 R1 = 1568 Ω R1 = 1588.33 Ω -0.012799607 0.000629592
0.002264031 Resistor #2 R2 = 1028 Ω R2 = 1022.1 Ω 0.005772429 0.000978378
Resistor #3 R3= 1484 Ω R3 = 1417.1 Ω 0.047209089 0.000705667
Measured
Parallel
Resistors
RT= 438 Ω RT= 441.69 Ω -0.008354276 0.002313636 0.002283105
Calculated
Parallel
Resistors
RT= 432.2200252 Ω RT= 432.22003 Ω 0 0.002283105 0.002313636
%
Difference -1.319628939 2.191007866 1.319628939 -1.33727602
Resistor #1 Resistor #2 Resistor #3 Parallel Resistors
Voltage Current Voltage Current Voltage Current Voltage Current
0 0.0000E+00 0 0.0000E+00 0 0.0000E+00 0 0
1 6.3000E-04 1 9.6000E-04 1 6.7000E-04 1 2.24E-03
2 1.2600E-03 2 1.9200E-03 2 1.3300E-03 2 4.49E-03
3 1.8900E-03 3 2.8900E-03 3 2.0000E-03 3 6.73E-03
4 2.5300E-03 4 3.8500E-03 4 2.6700E-03 4 8.98E-03
5 3.6200E-03 5 4.8200E-03 5 3.3300E-03 5 1.12E-02
6 3.7900E-03 6 5.7800E-03 6 1.0000E-03 6 1.35E-02
7 4.4200E-03 7 6.7500E-03 7 4.6700E-03 7 1.57E-02
8 5.0500E-03 8 7.1300E-03 8 5.3400E-03 8 1.80E-02
9 5.6900E-03 9 8.7000E-03 9 6.0100E-03 9 2.03E-02
10 6.3200E-03 10 9.6700E-03 10 6.6700E-03 10 2.25E-02
11 6.9500E-03 11 1.0650E-02 11 7.3400E-03 11 2.48E-02
12 7.5800E-03 12 1.1620E-02 12 8.0100E-03 12 2.71E-02
13 8.2200E-03 13 1.2610E-02 13 8.6800E-03 13 2.93E-02
14 8.8500E-03 14 1.3600E-02 14 9.3500E-03 14 3.16E-02
15 9.4800E-03 15 1.4610E-02 15 1.0020E-02 15 3.39E-02
Ohm’s Law Parts I & II Emily A. Gatlin
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16 1.0110E-02 16 1.5600E-02 16 1.0690E-02 16 3.61E-02
17 1.0750E-02 17 1.6590E-02 17 1.1360E-02 17 3.85E-02
18 1.1380E-02 18 1.7600E-02 18 1.2030E-02 18 4.08E-02
Resistors in Parallel
Current 5 volts 10 volts 15 volts
Total IT 1.12E-02 2.25E-02 3.39E-02
Resistor #1 I1 3.16E-03 6.32E-03 9.48E-03
Resistor #2 I2 4.83E-03 9.68E-03 1.46E-02
Resistor #3 I3 3.33E-03 6.67E-03 1.00E-02
Sum I1 + I2 + I3 1.13E-02 2.27E-02 3.41E-02
% Difference Total & Sum -0.706713781 -0.74988972 -0.46976
Power Supply VT 14.97
Resistor #1 V1 14.96
Resistor #2 V2 14.97
Resistor #3 V3 14.97
RESISTORS IN A SERIES
Band #1 Value Band #2 Value Band #3 Value Band #4 Value Tolerance
Resistor #1 Br 1 Red 5 Red 2 Silver 1500 10%
Resistor #2 Br 1 Black 0 Red 2 Silver 1000 10%
Resistor #3 Br 1 Green 5 Red 2 Gold 1500 5%
y = 0.0006x + 5E-05
y = 0.001x - 1E-04
y = 0.0007x - 0.0003
y = 0.0023x - 7E-05
-5.0000E-03
0.0000E+00
5.0000E-03
1.0000E-02
1.5000E-02
2.0000E-02
2.5000E-02
3.0000E-02
3.5000E-02
4.0000E-02
4.5000E-02
0 2 4 6 8 10 12 14 16 18 20
C
u
r
r
e
n
t
(
m
A
m
p
s)
Voltage (Volts)
Current vs. VoltageResistor #1
Resistor #2
Resistor #3
Ohm’s Law Parts I & II Emily A. Gatlin
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Ohmmeter values
Slope Values %Difference Inverse Slope
Inverse Sum
Resistor #1 R1 = 1568 R1 = 1588.33 -0.01279961 0.0006 2.000637755
Resistor #2 R2 = 1028 R2 = 1022.1 0.005772429 0.001
Resistor #3 R3= 1484 R3 = 1417.1 0.047209089 0.0007
Measured Series Resistors
RT= 4.08E+03 RT= 441.69 -0.67676128 4107.8 0.000243439
Calculated Series Resistors
RT= 4080 RT= 432.2200252 8.43963667 0.000243439 0.000245098
% Difference 0 2.191007866 -0.681372549
Resistor #1 Resistor #2 Resistor #3 Series Resistors
Voltage Current Voltage Current Voltage Current Voltage Current
0 0.0000E+00 0 0.0000E+00 0 0.0000E+00 0 0
1 6.3000E-04 1 9.6000E-04 1 6.7000E-04 1 2.40E-04
2 1.2600E-03 2 1.9200E-03 2 1.3300E-03 2 4.90E-04
3 1.8900E-03 3 2.8900E-03 3 2.0000E-03 3 7.30E-04
4 2.5300E-03 4 3.8500E-03 4 2.6700E-03 4 9.70E-04
5 3.6200E-03 5 4.8200E-03 5 3.3300E-03 5 1.21E-03
6 3.7900E-03 6 5.7800E-03 6 1.0000E-03 6 1.46E-03
7 4.4200E-03 7 6.7500E-03 7 4.6700E-03 7 1.70E-03
8 5.0500E-03 8 7.1300E-03 8 5.3400E-03 8 1.95E-03
9 5.6900E-03 9 8.7000E-03 9 6.0100E-03 9 2.19E-03
10 6.3200E-03 10 9.6700E-03 10 6.6700E-03 10 2.43E-03
11 6.9500E-03 11 1.0650E-02 11 7.3400E-03 11 2.68E-03
12 7.5800E-03 12 1.1620E-02 12 8.0100E-03 12 2.92E-03
13 8.2200E-03 13 1.2610E-02 13 8.6800E-03 13 3.16E-03
14 8.8500E-03 14 1.3600E-02 14 9.3500E-03 14 3.41E-03
15 9.4800E-03 15 1.4610E-02 15 1.0020E-02 15 3.65E-03
16 1.0110E-02 16 1.5600E-02 16 1.0690E-02 16 3.89E-03
17 1.0750E-02 17 1.6590E-02 17 1.1360E-02 17 4.14E-03
18 1.1380E-02 18 1.7600E-02 18 1.2030E-02 18 4.38E-03
Resistors in Series
Current 5 volts 10 volts 15 volts
Total VT 4.99E+00 9.98E+00 1.50E+01
Resistor #1 V1 1.92E+00 3.84E+00 5.75E+00
Resistor #2 v2 1.26E+00 2.51E+00 3.77E+00
Resistor #3 V3 1.81E+00 3.63E+00 5.45E+00
Sum I1 + I2 + I3 4.99E+00 9.98E+00 1.50E+01
% Difference Total & Sum 0.060156 0 1.19E-14
Ohm’s Law Parts I & II Emily A. Gatlin
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Power Supply IT 1.22E-03
Resistor #1 I1 1.22E-03
Resistor #2 I2 1.21E-03
Resistor #3 I3 1.21E-03
RESULTS In the first part of the experiment, the light bulbs failed to act as complete resistors. Therefore,
the calculations in the tables reflect moderately accurate calculations of the total resistance. Due to the
complications, the individual resistances failed to be calculated. The fourth section shows that the
relationship to the parallel resistors plays a role in the brightness of the light bulb. Here, the first light
bulb had the greatest brilliance. In the fifth section, the light bulb in parallel is the brightest. This
y = 1588.3x - 0.0715
y = 1022.1x + 0.1054
y = 1417.1x + 0.7083
y = 441.69x + 0.0323
y = 4107.8x + 0.0061
-2
0
2
4
6
8
10
12
14
16
18
20
0.0000E+005.0000E-031.0000E-021.5000E-022.0000E-022.5000E-023.0000E-023.5000E-024.0000E-024.5000E-02
Vo
ltag
e (v
)
Current (Amps)
Voltage vs. Current
Resistor #1
Resistor #2
Resistor #3
Resistors in Parallel
Resistors in Series
Linear (Resistor #1)
Linear (Resistor #2)
Linear (Resistor #3)
Linear (Resistors in Parallel)
Linear (Resistors in Series)
Ohm’s Law Parts I & II Emily A. Gatlin
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brightness is due to its configuration in parallel—it provides an alternative route for the current and
possesses a resistance that is the inverse of one of the other light bulbs configured in a series.
In the second part of the experiment, there was relatively little error and the calculated values
obtained from the slopes for the most part yielded accurate data. The sources of error that caused some
deviation from the measured values was due to the presence of the meters themselves and the variant
resistances that might be from mechanical or technical error. However, it adequately showed that the
relationship to the configuration of resistors highly contributes to the power consumption. Lastly, the
data demonstrated how Ohm’s law is a highly influential aspect to understanding the relationships
between current, voltage, and resistance.
CONCLUSION Overall, both parts of this lab demonstrated the relationship outlined by Ohm’s Law and fostered a
higher comprehension of the mechanisms driving circuit behavior. The direct relationships between
voltage, current, and resistance allow measurement of the voltage and current without resistance being
known. Additionally, the ability to manipulate voltage allowed the experiment to contain a sense of
systematic collection of data to provide a contextual experimental example of the relationships in Ohm’s
law. Moreover, the experiment also demonstrated how the different configurations of resistors, parallel
or in a series could play a role in the behavior of the circuit and its components. In conclusion, this lab
effectively helped grant a higher understanding of how circuits are governed by Ohm’s law.