Determination of temperature coefficient of resistance of a metal (Cu) using the Metre Bridge

When the bridge is balanced,

$$\frac{R_\theta}{R_B} = \frac{l}{100-l}$$

where:

• $R_B$ = resistance from the resistance box
• $R_\theta$ = resistance of the copper coil at temperature $\theta$
• $R_0$ = resistance of the coil at $0^\circ C$
• $\alpha$ = temperature coefficient of resistance

The resistance at temperature $\theta$ is given by:

$$R_\theta = R_0(1+\alpha \theta)$$

Therefore,

$$R_B \left(\frac{l}{100-l}\right)=R_0(1+\alpha \theta)$$

Rearranging,

$$\frac{l}{100-l} = \left(\frac{R_0\alpha}{R_B}\right)\theta + \frac{R_0}{R_B}$$

If $\dfrac{l}{100-l}$ is plotted against $\theta$:

• Gradient $= \dfrac{R_0\alpha}{R_B}$
• Intercept $= \dfrac{R_0}{R_B}$

Hence,

$$\alpha = \frac{\text{Gradient}}{\text{Intercept}}$$

1. Connect the circuit as shown in Figure 32.1.
2. Close switch $K_1$ and keep $K_2$ open.
3. Measure and record the initial temperature $\theta$.
4. Stir the water well and obtain the rough balance point.
5. Close switch $K_2$ and obtain the accurate balance point.
6. Measure and record the balancing length $l$.
7. Heat the water while stirring continuously.
8. For every increase of $10^\circ C$, measure the corresponding balancing length $l$.
9. Record about six sets of readings.