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Question

A wire of resistance 0.5Ωm1 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
π ohm
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B
π(π+2) ohm
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C
π(π+4) ohm
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D
(π+1) ohm
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Solution

The correct option is C π(π+4) ohm

Resistance of upper semicircle = Resistance of lower semicircle

0.5×(πR)=0.5πΩ
Resistance of wire AB =0.5×2=1Ω
Hence equivalent resistance between A and B
1RAB=10.5π+11+10.5πRAB=π(π+4)Ω

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