Question

The V-I graph for a conductor at temperatures $T_1$ and $T_2$ are shown in the figure, Then $(T_2-T_1)$ is proportional to :

• A. $tan2\theta$
• B. $sin2\theta$
• C. $cos2\theta$
• D. $cot2\theta$

Answer 1

The correct option is D $cot2\theta$

The slope of V-I graph gives resistance
$R_1=tan\theta ,R_2=tan(90-\theta )=cot\theta$
$R_1=R_0(1+\alpha T_1)$ and $R_2=R_0(1+\alpha T_2)$
$\therefore cot\theta -tan\theta =R_0\alpha (T_2-T_1)$
$\therefore T_2-T_1\propto \frac{cos\theta }{sin\theta }-\frac{sin\theta }{cos\theta }$
$\propto \frac{2(co{s}^2\theta -si{n}^2\theta )}{2sin\theta \cdot cos\theta }$
$\propto \frac{2cos2\theta }{sin2\theta }$
$\therefore T_2-T_1\propto cot2\theta$