A wire of resistance 0.5 Ohm/m is bent into a circle of radius 1 m. The same wire is connected across a diameter AB as shown in fig. what is the equivalent resistance between AB?
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Resistance of upper semicircle = Resistance of lower semicircle
\[=0.5\times (\pi R)=0.5\pi R \ \Omega\]
Resistance of wire AB $=0.5\times 2=1\Omega$
\[Hence \ equivalent \ resistance \ between \ A \ and \ B\]
\[\frac{1}{R_{AB}}=\frac{1}{0.5\pi }+\frac{1}{1}+\frac{1}{0.5\pi }\Rightarrow \frac{1}{R_{AB}}=\frac{\pi }{\pi +4}\Omega\]
