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Series and Parallel Combination of Resistors

A wire of res...

Question

A wire of resistance $0.5 Ω m^{- 1}$ 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

π

ohm

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π (π + 2)

ohm

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\frac{π}{(π + 4)}

ohm

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(π + 1)

ohm

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Solution

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

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

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