Physics 222 Ohm's Law Lab Report

Name: Emily A. Gatlin Partner: Whitney Heaston st Performed: January 21 , 2009 & January 28th, 2009 Date: 4 February 2009 Class: Physics 221, Section 004 T.A.: John Carruth

OHM’S LAW 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.

1 | Page

Ohm’s Law Parts I & II Emily A. Gatlin

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

potential difference (

―

times a

. 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 2|P a g e

Ohm’s Law Parts I & II Emily A. Gatlin

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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Ohm’s Law Parts I & II Emily A. Gatlin

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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Ohm’s Law Parts I & II Emily A. Gatlin

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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Ohm’s Law Parts I & II Emily A. Gatlin

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

P ART II VOLTAGE

CURRENT

P OWER

RESISTANCE

18

0.098

1.764 W

183.6734694

0.098

1.764

CURRENT

P OWER

BULB

1

18 P ART III VOLTAGE 6|P a g e

RESISTANCE

Ohm’s Law Parts I & II Emily A. Gatlin 18

0.292

5.256

0.292

2.628

0.292

2.628

VOLTAGE

CURRENT

P OWER

RESISTANCE

18

0.246

6.642

109.7560976

0.246

2.214

0.246

2.214

0.246

2.214

VOLTAGE

CURRENT

P OWER

RESISTANCE

18

0.128

2.304

140.625

0.128

0.576

35.15625

0.128

0.576

35.15625

0.128

1.152

70.3125

BULB

1

9 BULB

61.64383562

2

9 P ART IV

BULB

1

9 BULB

2

9 BULB

3

9 P ART V

BULB

1

4.5 BULB

2

4.5 BULB

3

9

Voltage Vs. Current

20 V o l t a g e

y = 132.71x - 3.2932

15 10 5 0 0

0.02

-5

EXPERIMENT PART II RESISTORS IN PARALLEL

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0.04

0.06

0.08 Current

0.1

0.12

0.14

0.16

Ohm’s Law Parts I & II Emily A. Gatlin 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

Inverse Slopes and Sums

%Difference

Resistor #1

R1 =

1568 Ω

R1 =

1588.33 Ω

-0.012799607

0.000629592

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

1.319628939

-1.33727602

% Difference

-1.319628939

Resistor #1 Voltage Current

2.191007866

Resistor #2 Voltage Current

Resistor #3 Voltage Current

0.002264031

Parallel Resistors 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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Ohm’s Law Parts I & II Emily A. Gatlin 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 IT I1 I2 I3

Total Resistor #1 Resistor #2 Resistor #3 Sum I1 + I2 + I3 % Difference Total & Sum Power Supply Resistor #1 Resistor #2 Resistor #3

VT V1 V2 V3

C 4.0000E-02 u r3.5000E-02 r3.0000E-02 e n2.5000E-02 t2.0000E-02

10 volts

15 volts

1.12E-02

2.25E-02

3.39E-02

3.16E-03

6.32E-03

9.48E-03

4.83E-03

9.68E-03

1.46E-02

3.33E-03

6.67E-03

1.00E-02

1.13E-02

2.27E-02

3.41E-02

-0.706713781

-0.74988972

-0.46976

14.97 14.96 14.97 14.97

Current vs. Voltage

Resistor #1

4.5000E-02

5 volts

y = 0.0023x - 7E-05

Resistor #2 Resistor #3

y = 0.001x - 1E-04

(

1.5000E-02 m A1.0000E-02 m5.0000E-03 p s0.0000E+00

y = 0.0007x - 0.0003 y = 0.0006x + 5E-05

)

-5.0000E-03 0

2

4

6

8

10

12

14

16

18

20

Voltage (Volts)

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%

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Ohm’s Law Parts I & II Emily A. Gatlin Slope Values

%Difference

Resistor #1

Ohmmeter values R1 = 1568

R1 = 1588.33

-0.01279961

Inverse Slope 0.0006

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 Calculated Series Resistors

RT= 4.08E+03

RT= 441.69

-0.67676128

4107.8

0.000243439

RT= 4080

RT= 432.2200252

8.43963667

0.000243439

0.000245098

% Difference

0

2.191007866

Resistor #1

Inverse Sum 2.000637755

-0.681372549

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 Total

Current VT

5 volts 4.99E+00

10 volts 9.98E+00

15 volts 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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Ohm’s Law Parts I & II Emily A. Gatlin Power Supply

IT

1.22E-03

Resistor #1

I1

1.22E-03

Resistor #2

I2

1.21E-03

Resistor #3

I3

1.21E-03

20 18

Voltage vs. Current y = 1588.3x - 0.0715

y = 4107.8x + 0.0061 16 14

Voltage (v)

12 10

y = 441.69x + 0.0323

y = 1022.1x + 0.1054 y = 1417.1x + 0.7083 Resistor #1 Resistor #2

Resistor #3 Resistors in Parallel Resistors in Series

8 6 4

Linear (Resistor #1) Linear (Resistor #2) Linear (Resistor #3) Linear (Resistors in Parallel) Linear (Resistors in Series)

2 0 0.0000E+005.0000E-031.0000E-021.5000E-022.0000E-022.5000E-023.0000E-023.5000E-024.0000E-024.5000E-02 -2 Current (Amps)

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

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Ohm’s Law Parts I & II Emily A. Gatlin

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.

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