Question

A uniform thin consonant wire of resistance '$R$' is bent like a circle. $P$ and $Q$ are two points on the wire such that the arc $PQ$ subtends and angle $\theta$ at the centre. Effective resistance between $P$ and $Q$ is

• A. $\frac{R\theta }{4\pi }(\pi -\theta )$
• B. $\frac{R\theta }{\pi +8}$
• C. $\frac{R\theta }{2{\pi }^2}(2\pi -\theta )$
• D. $\frac{R\theta }{4{\pi }^2}(2\pi -\theta )$

Answer 1

Answer: (D)

$\frac{R\theta }{4{\pi }^2}(2\pi -\theta )$

$R_1=\frac{\theta }{2\pi }R{R}_2=(1-\frac{\theta }{2\pi })R$

These two are in series.

$R_{eff}=\frac{(1-\frac{\theta }{2\pi })\frac{\theta }{2\pi }R\times R}{R}=\frac{(2\pi -\theta )\theta R}{4{\pi }^2}$