Determine the Resistivity of a Wire Using a Metre Bridge – Class 12 Practical

Aim

To determine the resistivity (specific resistance) of a given wire by using a metre bridge (Wheatstone bridge) to measure the resistance of a known length of wire and calculating resistivity from measured diameter and length.

Apparatus Required

Metre bridge, a test wire of known length, low-value resistance box, galvanometer and jockey, one-way key, cell or battery eliminator, thick connecting wires, sand paper, and screw gauge.

Theory

To find the resistance of the wire

A metre bridge works on the principle of the Wheatstone bridge.
The unknown resistance X is placed in the right gap, while a known resistance R from the resistance box is in the left gap.

When the bridge is balanced (null deflection on galvanometer):

[ \frac{P}{Q} = \frac{L}{100 - L} ]

[ \frac{P}{Q} = \frac{R}{X} ]

[ X = \frac{R(100 - L)}{L} ]

Specific Resistance (Resistivity)

The resistivity ( \rho ) of the wire is:

[ \rho = \frac{RA}{L} = \frac{\pi r^2 X}{L} ]

where
• r = radius of wire
• L = length of wire
• X = resistance of wire

Procedure

1. Measure the diameter of the wire using a screw gauge and calculate its radius.
2. Clean insulation from connecting wires using sand paper. Press all resistance box plugs tightly.
3. Set up the circuit as shown, with the unknown resistance in one gap.
4. Introduce resistance R from the resistance box.
   Touch the jockey first at A and then at C.
   Observe the galvanometer deflection direction.
   Ensure the jockey touches the wire only for a fraction of a second.
5. Adjust R so that the null point lies between 30 cm and 70 cm.
6. Repeat step 4 for four different values of R.
7. Interchange resistances S and R and repeat the same procedure.
   Ensure the same length of wire is in the gap after interchange.

Precautions

1. Ensure all connections are tight and wires are cleaned before connecting.
2. The jockey should not be pressed hard and must slide gently.
3. Balance point should lie near the midpoint of the wire.
4. Percentage error should be kept minimal.

Sources of Error

1. Non-uniform thickness of the wire.
2. Loose resistance box plugs.
3. Heating of wires due to continuous current.
4. Contact resistance due to improper connections.