BACKGROUND: A straightforward method to determine the resistance of a resistor makes use of Ohm’s law. The current through a resistor can be measured by an ammeter and the voltage across the resistor can be measured by a voltmeter. Two different circuit diagrams for the experiment are shown in the figures below:
A
R
V
+ −
Figure 4.1:Ohm’s Law Circuit I.
A
R
V
+ −
Figure 4.2:Ohm’s Law Circuit II.
An ammeter is a very low-resistance device (ideally resistance should be zero) and a voltmeter is a very high-resistance device (ideally resistance should be infinite). In the circuit in Fig. 4.1, the ammeter A gives the true current through the resistance whereas the voltmeter V measures the voltage across the resistance plus the voltage across the ammeter.
For this circuit, the ratio V /I will be greater than the true resistance of the resistor, R .
In the circuit of Fig. 4.2, on the other hand, the voltmeter V gives the true voltage across the resistor whereas the ammeter A measures the current through the resistor plus the
Networks and Wheatstone Bridge: page 1

current through the ammeter. For this circuit, the ratio V /I will be smaller than R .
These considerations lead us to the conclusion that an ideal ammeter has a zero resistance
(so the voltage across it is zero) and an ideal voltmeter has an infinite resistance (so the current through it is zero). These ideal conditions cannot be achieved, but they can be closely approached.
A circuit to determine the resistance of a resistor accurately has been devised by
Wheatstone and is called the Wheatstone bridge. When properly balanced, the measuring instrument reads zero and therefore avoids the pitfalls discussed earlier.
OBJECT: To measure the resistance of a given conductor using the slide-wire Wheatstone bridge and to determine the specific resistance or resistivity of the material of the conductor.
APPARATUS: Slide-wire Wheatstone bridge, dry cell, galvanometer, standard decade resistance box, switch with resistor, tap key, resistance spools, connecting wires.
THEORY: A Wheatstone bridge is a circuit consisting of four resistors as shown in Fig. 4.3.
The value of one unknown resistance can be computed from the remaining three resistances which are known.
i
2 i
1 i
3
+ −
R
3
R
1
R
2
G
R
4 i
4
Figure 4.3:Heatstone Bridge.
When the bridge is balanced, no current flows through the galvanometer G. Hence the current i
1 through R
1 is the same as the current i
2 through R
2
, and the current i
3 through R
3 is the same as the current i
4 through R
4
. In other words, in a balanced bridge we have i
1
= i
2
, and i
3
= i
4
.
(1)
Next, the potential drop across R
1 is equal to that across R
3
, so that i
1
R
1
= i
3
R
3
.
Similarly, the potential drop across R
2 is equal to that accross R
4
:
(2) i
2
R
2
= i
4
R
4
, or i
1
R
2
= i
3
R
4
, (3)
Networks and Wheatstone Bridge: page 2

using Eq. (1).
Dividing Eq. (2) by Eq. (3) yields the final relation:
R
1
R
2
=
R
3
R
4
.
(4)
Therefore, if any three of the resistances in Fig. 4.3 are known, the fourth one may be calculated by using Eq. (4).
In the slide-wire form of the bridge, as shown in Fig. 4.3, the resistances R
3 and
R
4 are replaced by the lengths AB and CB, respectively, of a uniform wire AB with a sliding contact key at C. Since the wire is uniform, the resistances of the two portions are proportional to their lengths. Hence, the ratio of resistances R
3
/R
4 is equal to the ratio of lengths AC/CB. If R
1 is represented by the unknown resistance X , and R
2
, by the known resistance R , Eq. (4) becomes:
X
R
=
AC
CB
, or X =
AC
CB
R , from which the value of the unknown resistance, X , may be calculated.
D
(5)
G
X R
K
1
A
C
K
+ − K
2
B
Figure 4.4:Experimental Setup.
It is found that the resistance of a conductor depends on the material from which it is made, its length, its cross-sectional area, and its temperature. For constant temperature the resistance, R in Ohms, of a uniform wire is given by
R =
ρL
A
.
(6) where L is the length of the wire in meters, and A is its cross-sectional area in square meters. The proportionality factor ρ is known as the specific resistance or resistivity of the conductor. It is constant for a given temperature and depends only on the nature of the material. Thus theresistivity of a substance is the resistance per unit length for a unit cross-sectional area. Its units are Ohm-meters.
In order to find ρ it is necessary only to determine the resistance of a known length of wire of given radius. The resistivity is then calculated from Eq .(6).
Networks and Wheatstone Bridge: page 3

PROCEDURE:
1. Connect the circuit as shown in Fig. 4.4, with connecting wires as short as possible. A standard resistance box is used for R. Have the circuit checked out by the instructor.
2. Contact is made to the wire by closing the contact key K at C. Do not slide this key along the wire while it is pressed down in order to avoid scraping and causing it to become nonuniform. Before closing the tap key K
1
, make sure that the 10,000-ohm protective resistor is connected in series with the galvanometer.
3. Activate the bridge by closing the key K
2
.
It is very important that K
2 is closed only when an observation is being made . Move (do not slide!) the contact key K to about the middle of the slide-wire. Adjust R so that when the key K is pressed down, the galvanometer shows the least possible deflection. Now remove the protective resistance by closing the shunt K
1
, and find the null point by shifting the sliding contact until no deflection is observed in the galvanometer.
4. Record the resistance R and lengths AC and CB.
5. Record the length L of the wire and the gauge (translate it into diameter D) of the spool wire and the material of the wire.
6. Repeat these procedure for a spool of different material of wire.
Calculations and Results:
Calculate the unknown resistance X : and the resisitivity ρ of the spool wire:
AC
X =
CB
R .
(7)
ρ =
A
L
X =
πD
2
X .
4 L
(8)
Compare ρ with the accepted value, which may be obtained from the instructor, through a percent-error calcualtion.
Networks and Wheatstone Bridge: page 4