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Measurement of Resistance:
Ammeter – Voltmeter Methods

The magnitude of resistance can be measured by different methods. One method is to measure the voltage drop V across a resistance n a circuit with a voltmeter and the current I through the resistance with an ammeter. Then using Ohm’s Law, R = V/I. However the ratio of the measured voltage and current does not give an exact value of the resistance because of the resistance of the meters.

This problem is eliminated when one compares the resistance with a standard resistance in a Wheatstone Bridge circuit. In this experiment, the first method for measuring the resistance will be investigated.

Ammeter – Voltmeter Methods:

Two circuits will be used to measure the resistance using this method. The first circuit is shown below.

In this circuit, the current measured by the ammeter divides between the resistance R and the voltmeter in parallel. The voltmeter is a high resistance instrument and draws little current as long as the voltmeter resistance Rv is much greater than R. Thus,

if > R

For a more accurate measurement, the resistance of the voltmeter must be taken into account. The current drawn by the voltmeter is Iv = V/Rv and the total current measured by the ammeter is

I = IR + Iv

The true current through the resistance is

IR = I – Iv

and from Ohm’s Law

The second circuit is shown below.

In this case, the ammeter measures the current through the resistance alone, but the voltmeter measures the voltage drop across both the resistance and the ammeter. Since the ammeter is a low resistance instrument, then the voltage drop across the ammeter (Va = I Ra) is small compared to that across R. Then

if Ra < R

where Ra is the resistance of the ammeter.

If the resistance of the ammeter is taken into account, then

V = VR + Va = IR + IRa

= I(R + Ra) = I R’

where R’ = R + Ra. Since R’ = V/I, then

R = R’ – Ra = V/I - Ra

STUDENT OUTCOMES

Through this experiment, students will learn:

-two ways of measuring resistance with an ammeter and a voltmeter and explain how they differ

-how to connect ammeter and a voltmeter in a circuit

MATERIALS

Power Supply / Vernier Circuit Board
Ammeter / Rheostat
Voltmeter / Wires

PRELIMINARY QUESTIONS:

1. When one is measuring resistance with an ammeter and voltmeter, is the resistance given exactly by R = V/I? Explain.

2. Is an ammeter connected in series or parallel with a circuit component? Explain.

3. Is a voltmeter connected in series or parallel with a circuit component? Explain.

PROCEDURE:

1. Setup the first circuit, where R is the unknown resistance and Rh is the rheostat (variable resistance). Do not connect the power supply until the instructor/peer mentor has checked it. (Use the 10 ohm resistor on the circuit board for R).

2. Familiarize yourself with the ammeter and voltmeter. There are three scale connections with the black binding post common for the three scales. It is good practice to start with the highest scale to prevent damaging the instrument. The scale setting may be changed to a lower scale after the general magnitude of the measurement is known.

Attention should also be given to the proper connection of the meters. Connect + to + and – to -.

3. The current in the circuit is changed by varying the rheostat resistance Rh. This is done by sliding the rider to a new position. Activate the circuit and take three different readings of the ammeter and the voltmeter corresponding to the different rheostat settings. Be sure to use one scale setting for the three data points. Record the data in Data Table 1. Deactivate the circuit.

4. Record the resistance of the voltmeter for the scale setting used in the acquisition of the data. The voltmeter resistance in ohms is approximately 1000 times the scale setting in volts.

5. Set up the second circuit. This can be accomplished by changing only one wire in the first circuit.

6. Repeat step 3 and record data in Data Table 2.

7. Repeat steps 1 – 6 for the 51 ohm resistor on the circuit board. Record its accepted value and record data on Data Table 3 and 4.

DATA TABLES:

TABLE 1: R = ______ohms Rv = ______Ohms

Rheostat Setting / V ( Volts) / I (Ampere) / R (ohms)
1
2
3

Average R = ______

% error = ______

TABLE 2: R = ______ohms

Rheostat Setting / V ( Volts) / I (Ampere) / R (ohms)
1
2
3

Average R = ______

% error = ______

TABLE 3: R = ______ohms Rv = ______Ohms

Rheostat Setting / V ( Volts) / I (Ampere) / R (ohms)
1
2
3

Average R = ______

% error = ______

TABLE 4: R = ______ohms

Rheostat Setting / V ( Volts) / I (Ampere) / R (ohms)
1
2
3

Average R = ______

% error = ______

DATA ANALYSIS:

1. Using Ohms Law, compute the value of R for Tables 1 – 4. Find the average value and the % error.

2. For Tables 1 and 3, will the computed value of R be closer to the actual value if the resistance of the voltmeter was taken into account? Explain. If it does, what will be the computed value of R for each table?

3. For Tables 2 and 4, will the computed value of R be closer to the actual value if the resistance of the ammeter was taken into account? Explain. Compute the ammeter resistance.

QUESTIONS:

1. The ideal ammeter would have zero resistance and an ideal voltmeter would have an infinite resistance. Why would this be the ideal case? Explain.

2. Which circuit arrangement in the ammeter – voltmeter methods had the smallest error? Explain.

3. The true resistance is measured by considering the ammeter resistance and the apparent resistance is measured using Ohm’s Law. Is the true resistance larger or smaller than the apparent resistance in Tables 2 and 4? Explain.

4. The true resistance is measured by considering the voltmeter resistance and the apparent resistance is measured using Ohm’s Law. Is the true resistance larger or smaller than the apparent resistance in Tables 1 and 3? Explain.

5. Why should the wires connecting the resistances be as short as possible? Explain.