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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 R v is much greater than R.
Thus,
if Rv > R
R V / I
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
R
V
V
V


I R I  IV I  V
RV
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
R V I
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
Ammeter
Rheostat
Vernier Circuit Board
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 R h 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 R h. 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 value 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
Rheostat Setting
Rv = _______Ohms
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
Rheostat Setting
Rv = _______Ohms
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.