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Measurement of Resistance:
Ammeter – Voltmeter Methods and
Wheatstone Bridge Method
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 two methods for measuring the resistance will be investigated.
Ammeter – Voltmeter Methods:
Two circuits will be used to measure the resistance using this method.
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 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
Another 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
R V I
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
Wheatstone Bridge Method:
The Wheatstone Bridge circuit consists of four resistors, a battery and
a galvanometer. The basic circuit is shown below and the values of R1,
R2, and Rs are all known and Rx is unknown.
When the circuit is closed, the bridge is balanced by adjusting the
standard resistance Rs until there is no current through the
galvanometer branch (galvanometer reads zero). When the bridge is
balanced, points b and c in the circuit are at the same potential;
current I1 flows through both Rs and Rx and current I flows through
both R1 and R2. Also the voltage drop across Rs is equal to the voltage
drop across R1
Vab = Vac
and Vbd = Vcd
This can also be written as
I1 Rx = I2 R2
I1 Rs = I2 R1
Dividing one equation by the other, one gets
R 
Rx   2  Rs
 R1 
So when the bridge is balanced, the unknown resistance Rx can be
obtained in terms of the known resistances.
The slide wire form of the Wheatstone bridge is shown below. The line
ad represents a wire and C is a contact key that slides along the wire
to divide the wire into L1 and L2. Since the resistance of the wire
segments are proportional to the lengths of the wire, then
R2 L2

R1 L1
and
L 
Rx   2  Rs
 L1 
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
- the basic principle and operation of the Wheatstone Bridge
- relative accuracy of the measured resistance when using the
ammeter-voltmeter methods and the Wheatstone Bridge
MATERIALS
Power Supply
Ammeter
Voltmeter
Rheostat
Resistance Box
Vernier Circuit Board
Wheatstone Bridge
Galvanometer
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 an voltmeter connected in series or parallel with a circuit
component? Explain.
4.
Why is the Wheatstone Bridge called a “null” instrument?
5. When the galvanometer in a Wheatstone bridge circuit shows no
deflection, why are the voltages across opposite branches on each side
of the galvanometer necessarily equal?
PROCEDURE:
Ammeter – Voltmeter Method
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 -.
Do not connect the power supply until the instructor/peer mentor has
checked it.
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.
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.
Wheatstone Bridge:
1. Set – up the Wheatstone Bridge as shown above. Use the 10 ohm
resistor as Rx. The wires connecting the resistances and the bridge
should be as sort as possible. The decade resistance box will be used
for Rs. Set Rs to be initially equal to Rx. Have the instructor/peer
mentor check the circuit before activating the power supply.
2. Turn on the power supply and balance the bridge by moving the
slide wire contact until the galvanometer reads zero. Disconnect the
power supply from the circuit and record L1, L2, and Rs. Record your
values in Table 5.
3. Repeat steps 1 -2 for Rs setting of (a) 3Rx and (b) 0.3 Rx.
4. Repeat steps 1 – 3 for Rx = 51 ohms. Record your values in Table 6.
DATA TABLE:
TABLE 1: R = ______ohms
Rheostat Setting
V ( Volts)
Rv = _______Ohms
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
V ( Volts)
Rv = _______Ohms
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 = _______________
Table 5: Accepted value of Rx = ____________ ohms
Rs (
)
L1 (
)
L2 (
)
Rx (
)
Rx (
)
Table 6: Accepted value of Rx = ____________ ohms
Rs (
)
L1 (
)
L2 (
)
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. Deduce the ammeter resistance.
4. For Tables 5 and 6, compute the value of Rx and find the average
value. Compare the average value with the accepted value by finding
the percent error.
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 and the
Wheatstone bridge be as short as possible? Explain.
6. Why is does one need to turn off the circuit in-between
measurement when using the Wheatstone bridge? Explain.
7.
If the power supply was connected in reverse, where the positive
terminal is connected to d instead of a, will the outcome be different?
Explain.
8.
Suppose the slide wire on the bridge does not have a uniform
cross sectional area. How would this affect your measurement?
9. Compare the two methods for measuring resistances. State the
advantages and disadvantages of each method.