Question

Assertion The $V$ -i graph for a conductor at temperatures $T_1$ and $T_2$ is shown in figure, then $\left(T_2-T_1\right)$ is proportional to $\cot 2\theta$.
Reason Resistance of conductor decrease with rise in temperature.

• A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion
• B. If both Assertion and Reason are true but Reason is not correct explanation of the Assertion
• C. If Assertion is true but Reason is false
• D. If Assertion is false hut the Reason is true

Answer 1

Answer: (B)

From the relation for $V$ -i graph
$R=\tan \theta =R_0(1+\alpha T)$
where, $\theta$ is angle made by $V$ -i graph with $i$ axis.
So, $R_1=\tan \theta =R_0\left(1+\alpha T_1\right)$ ......(i)
$R_2=\tan \left(90^{\circ }-\theta \right)=\cot \theta$
$=R_0\left(1+\alpha T_2\right)$ .......(ii)
So, $\cot \theta -\tan \theta =R_0\alpha \left(T_2-T_1\right)$
or $\frac{\cos \theta }{\sin \theta }-\frac{\sin \theta }{\cos \theta }=R_0\alpha \left(T_2-T_1\right)$
$\frac{{\cos }^2\theta -{\sin }^2\theta }{\sin \theta \cos \theta }=\frac{2\cos 2\theta }{\sin 2\theta }=R_0\alpha \left(T_2-T_1\right)$
Hence, $T_2-T_1\propto \cot 2\theta$