Figure shows a metre bridge, wire AC has uniform cross-section. The length of wire AC is 100 cm. X is a standard resistor of 4Ω and Y is a coil. When Y is immersed in melting ice the null point is at 40 cm from point A. When the coil Y is heated to 100°C, a 78 Ω resistor has to be connected in parallel with Y in order to keep the bridge balanced at the same point. Temperature coefficient of resistance of the coil is :

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Figure shows a metre bridge, wire AC has uniform cross-section. The length of wire AC is 100 cm. X is a standard resistor of 4Ω and Y is a coil. When Y is immersed in melting ice the null point is at 40 cm from point A. When the coil Y is heated to 100°C, a 78 Ω resistor has to be connected in parallel with Y in order to keep the bridge balanced at the same point.

Temperature coefficient of resistance of the coil is :

6.3 × 10^–4 K^–1

4.3 × 10^–4 K^–1

8.3 × 10^–4K^–1

2.3 × 10^–4 K^–1

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$\frac{x}{R_{0}} = \frac{ℓ}{100 - ℓ}$
Since null point remains unchanged
$\frac{x}{R^{'}} = \frac{40}{60} \Rightarrow R^{'} = 6 Ω$
and $6 = \frac{78 R_{t}}{R_{t} + 78} \Rightarrow R_{t} = 6.5 Ω$
$α = \frac{R_{t} - R_{0}}{R_{0} t} = 8.3 \times 10^{- 4} k^{- 1}$

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