Meter Bridge Experiment with Temperature Dependence of Resistance

To evaluate the given statements, we consider the working principle of a meter bridge, which is based on the balanced Wheatstone bridge condition:

$\frac{X}{R} = \frac{l}{100 - l}$

where:

• $X$ is the unknown resistance (usually placed in one of the gaps),
• $R$ is the known standard resistance (placed in the opposite gap),
• $l$ is the balancing length from the left end corresponding to the null point.

Analysis of STATEMENT-2:
The electrical resistance of a metal is given by:
$R(T) = R_0(1 + \alpha \Delta T)$
Since the temperature coefficient of resistance $\alpha$ is positive for metals, the resistance of a metal increases with an increase in temperature.
Therefore, STATEMENT-2 is True.

Analysis of STATEMENT-1:
When the unknown metallic resistance $X$ is placed in an enclosure maintained at a higher temperature, its resistance increases:
$X' > X$

For the null point to be obtained at the same position as before, the balancing length $l$ must remain unchanged. This requires the ratio of resistances to remain constant:
$\frac{X'}{R'} = \frac{X}{R} \implies R' = R\left(\frac{X'}{X}\right)$

Since $X' > X$, the new value of the standard resistance $R'$ must satisfy:
$R' > R$

Hence, to keep the null point at the same location, the value of the standard resistance must be increased, not decreased.
Therefore, STATEMENT-1 is False.

Conclusion:

• STATEMENT-1 is False.
• STATEMENT-2 is True.

This corresponds to Option D.