Q.
The effective resistance between points $P$ and $Q$ of the electrical circuit shown in the figure.
A) $\frac{2Rr}{R + r}$
B) $\frac{8R(R + r)}{(3R + r)}$
C) $2R + 4r$
D) $\frac{5R}{2} + 2R$
Explanation
(a) In the circuit arrangement $PSTQ$ is a balanced Wheatstone bridge, hence resistance $2R$ joined in arm $AB$ be omitted. Similarly, resistance $2R$ joined in arm $BC$ may also be omitted.
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$\therefore\frac{1}{R_{eq}} = \frac{1}{4R} + \frac{1}{2r} + \frac{1}{4R} = \frac{\mu + 2R + \mu}{4\mu R} = \frac{(R + r)}{2Rr}$
$\Rightarrow \ R_{eq} = \frac{2Rr}{R + r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.