A wire of resistance0.5Ωm−1is 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 Cπ(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+10.5π⇒RAB=π(π+4)Ω