Ohm's Law

June 19, 2000

Walter A. Dupre, Jr.

Physics
1st Period

Partner: Connie Dupre

Purpose:

The objective of this lab is to apply Ohm's Law to both series and parallel DC circuits. In addition, a DC voltmeter and a DC ammeter must be used properly in order to correctly measure the current and voltage present in the two circuits that are to be built. Using the two measured quantities of current and voltage, the resistance of the circuits can be calculated by applying Ohm's Law.

Concepts:
Current Electricity
Ohmís Law
Series Circuits
Parallel Circuits

Equipment:

Measuring Device

Quantity Measured

Smallest Scale Division

DC milliameter

Amperes

10 mA

DC voltmeter

Voltage

0.3 V

Other Equipment:†

  1. Fixed wire-bound resistors of 125 ohms and 250 ohms (+) 5% mounted on board
  2. Double-pole, single throw switch
  3. 2power leads with large lugs ( 1 - black, 1 - red )
  4. 6 connecting leads (assorted colors)†

Data:

Current (Amps)

Voltage (Volts)

Resistance (Ohms)

I

I1

I2

V

V1

V2

R

R1

R2

Series

0.035

0.035

0.035

12.0

3.9

8.0

342.9

111.4

228.6

Parallel

0.140

0.100

0.050

12.0

12.0

12.0

85.7

120

240

Sample Calculations:

1. ††† V = IR†††

R = ?

R = V/I

I = 0.035 A

R = 12 V / 0.035 A

V = 12 V

R = 342.9 W

2. ††† R = R1 + R2†††

R = ?

R = R1 + R2

R1 = 111.4W

R = 111.4W + 228.6W

R2 = 228.6W

R = 340.0 W

The two values compare favorably. In fact if significant digits are considered calculation 1 and calculation 2 both compute to 340 ohms.†

3. ††† V = IR†††

R = ?

R = V/I

I = 0.140 A

R = 12 V / 0.140 A

V = 12 V

R = 85.7 W

4. ††† 1/R = 1/R1 + 1/R2

R = ?

1/R = 1/R1 + 1/R2

R1 = 120.0W

1/R = 1/120W + 1/240W

R2 = 240.0W

1/R = 0.0083W + 0.0042W

1/R = 0.0125W

R = 1/0.0125W

R = 80W

For the parallel combination the two methods of calculating "R" provided values that were noticeably different from each other. This was expected, however, because the sum of individual amperages for I 1 and I2 was greater than the value for I that was measured directly from the circuit.

Error Analysis:

1) A) For the series connection: †††††† % Error = |accepted "R" - calculated "R"| / accepted "R"

% Error = ?

% Error = |accepted "R" - calculated "R"| / accepted "R"

accepted "R" = 375W

% Error = |375W - 342.9W| / 375W

calculated "R" = 342.9W

% Error = 0.086

Error = 8.6 %

†††††† B) For the parallel connection: †††††††††††† Error = 2.9 %

2) For this particular lab the amount of error falls within acceptable limits.

Conclusions:

The numerical results obtained from using Ohm's Law (V = IR) to calculated the resistance in a circuit, utilizing measured quantities for current and voltage, are close enough to the accepted values to validate this experiment. While there is some discrepancy in the accepted and calculated values this can be reasonably explained by the presence of random error in the experiment.

According to Ohm's Law, in electrical circuits there is a relationship between current, voltage, resistance, and power dissipated. It is further understood that if two of the quantities are known one or both of the other quantities can be determined. In this lab a voltmeter and milliammeter were respectively used to measure the voltage across and the current through a given circuit. Once these values were measured using the appropriate instrumentation the resistance in the circuit was computed using Ohm's Law.

The lab also illustrates the differences between series and parallel circuits by observing the results obtain using the two different types of circuits. This required knowledge of the formulas for series and parallel circuits to understand why different values for "R", "I", and "V" were obtained in spite of the fact that the physical elements present in each circuit were identical.

Comparing the numerical results obtained in this experiment to the accepted values proves that the lab supports the experimental theory. The accepted resistance of the resistors connected in series is 375 ohms. The calculated values using Ohm's Law and the formula for series circuits, in which the total resistance of resistors in series is equal to the sums of the individual resistances, is 342.9 ohms and 340 ohms respectively. Individually R1 has an accepted value of 125 ohms and R2 has an accepted value of 250 ohms; however, using experimental data R1 was calculated to be 111.4 ohms and R2 was calculated to be 228.6 ohms. The percent error for the total resistance of the series circuit was calculated to be 8.6 %.

Although these differences may appear a little high a deeper analysis of the numbers rejects this notion. The current measured using the milliammeter was 35 mA. Ohm's Law can be used to determine the theoretical value of "I" that should have been obtained. This is possible because it is known that the accepted values for the total resistance of the circuit is 375 ohms. Likewise, it is accepted that the voltage supplied to the entire circuit from the wall output is 12 V. Using these values a calculated theoretical current of 32 mA is obtained. For readings obtained from the milliammeter a difference of 3 mA appears to be more than acceptable.

However, there are other sources of error that may have contributed to the 8.6 % error. The age of the resistors used in the experiment, not to mention the handling they have received over the years, makes it quite possible that the resistance is slightly different than 375 ohms stated. Another possible source of error comes from the use of the milliammeter and voltmeter in the circuit. Although the resistance of each is not supposed to affect the circuit, the presence of the milliammeter and voltmeter cannot be discounted.

Similar results were obtained when measuring the parallel circuit. The accepted total resistance of the parallel circuit is 83.3 ohms. The calculated values using Ohm's Law and the formula for parallel circuits, in which the total resistance of resistors in parallel is equal to the reciprocal of the sum of the reciprocals of the individual resistances, is 85.7 ohms and 80 ohms respectively. Individually R1 has an accepted value of 125 ohms and R2 has an accepted value of 250 ohms; however, using experimental data R1 was calculated to be 120 ohms and R2 was calculated to be 240 ohms. The percent error for the total resistance of the series circuit was calculated to be 2.9 %.

The reasons for error in the parallel circuit are the same as the reasons for error in the series circuit. However, in spite of this, all the results calculated for the parallel circuit were much closer to the accepted value than all the comparable results calculated for the series circuit. This may be attributed to the fact that the single measurement of the current read for the series circuit was in error more than the current readings taken for the parallel circuit. This is especially possible since the series current measurement was in between two scaled divisions on the milliammeter and was therefore subject to more uncertainty than the measurements for the current in the parallel circuit, which fell directly on scaled divisions of the milliameter.

Once again, taking into account all the possible sources of error and uncertainty, this experiment, in which resistance was calculated based on measurements of current and voltage obtained using a milliammeter and a voltmeter, proves that Ohm's Law is fundamental to an understanding of the relationships inherent in electrical circuit theory.

††

Questions:

  1. How was the accepted value of 83.3 ohms in Calculation #4 obtained?
  2. The accepted value of 83.3 ohms was obtained using the formula for parallel circuits,
    †††††††††††††††† 1/R = 1/R1 + 1/R2. †

    R = ?

    1/R = 1/R1 + 1/R2

    R1 = 125.0W

    1/R = 1/125W + 1/250W

    R2 = 250.0W

    1/R = 0.008W + 0.004W

    1/R = 0.012W

    R = 1/0.012W

    R = 83.3W

  3. Why should the milliameter and voltmeter be read simultaneously?
  4. The values for current and voltage are not independent of each other for a circuit. Slight changes in one value can have quite visible effects in the other. Therefore to insure proper readings in both instruments it is necessary to read them simultaneously. If the two instruments are read at different times and slight changes to the circuit have occurred in that time interval, the two readings may not coordinate; therefore, giving incorrect values for any calculations made from those two measurements. †

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