Question

A wire of resistance $0.5\Omega m^{-1}$ is bent into a circle of radius 1 m. An identical wire is connected across a diameter AB as shown in fig. The equivalent resistance is

• A. $\pi$ ohm
• B. $\pi (\pi +2)$ ohm
• C. $\frac{\pi }{(\pi +4)}$ ohm
• D. $(\pi +1)$ ohm

Answer 1

The correct option is C $\frac{\pi }{(\pi +4)}$ ohm


Resistance of upper semicircle = Resistance of lower semicircle
$0.5\times \left(\pi R\right)=0.5\pi \Omega$
Resistance of wire AB $=0.5\times 2=1\Omega$
Hence equivalent resistance between A and B
$\frac{1}{R_{AB}}=\frac{1}{0.5\pi }+\frac{1}{1}+\frac{1}{0.5\pi }\Rightarrow R_{AB}=\frac{\pi }{(\pi +4)}\Omega$