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

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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


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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


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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.


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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.


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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



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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


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


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


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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


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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



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


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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


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Power Supply IT 1.22E-03

Resistor #1 I1 1.22E-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 (Resistors in Parallel)

Linear (Resistors in Series)


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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.

Physics 222 Ohm's Law Lab Report

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