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Q.
A uniform wire of resistance 36 ohm is bent in the form of a circle. The effective resistance across the points $A$ and $B$ is
Current Electricity
Solution:
Let $R$ be the resistance of total length of circular wire then $R=36\, \Omega$.
The resistance of smaller arc $A B$
$R_{1}=R / 6=36 / 6=6\, \Omega$
The resistance of bigger arc $A B$
$R_{2}=5 R / 6=5 \times 36 / 6=30\, \Omega$
Now, $R_{1}$ and $R_{2}$ are in parallel in between points $A$ and $B$.
So, effective resistance between $A$ and $B$
$=\frac{6 \times 30}{6+30}=5\, \Omega$
