Question

The V-i graph for a conductor at temperature $T_1$ and $T_2$ are as shown in the figure. $(T_2-T_1)$ is proportional to

• A. $cos2\theta$
• B. $sin\theta$
• C. $cot2\theta$
• D. $tan\theta$

Answer 1

The correct option is C $cot2\theta$

As we know, for conductors resistance $\propto$ Temperature.
From figure $R_1\propto T_1\Rightarrow tan\theta \propto T_1\Rightarrow tan\theta =k{T}_1$ ...........(i) (k = constant)
and $R_2\propto T_2\Rightarrow tan({90}^{\circ }-\theta )\propto T_2\Rightarrow cot\theta =k{T}_2$ ...........(ii)
From equation (i) and (ii) $k(T_2-T_1)=(cot\theta -tan\theta )$
$(T_2-T_1)=(\frac{cos\theta }{sin\theta }-\frac{sin\theta }{cos\theta })=\frac{(co{s}^2\theta -si{n}^2\theta )}{sin\theta cos\theta }=\frac{cos2\theta }{sin\theta cos\theta }=2cot2\theta \Rightarrow (T_2-T_1)\propto cot2\theta$