The effective resistance between points P and Q of the electrical circuit shown in the figure is [2002]

Question

Smart Achievers · Accepted Answer

(1)

The circuit above and below the axis POQ is symmetrical and represents a balanced Wheatstone bridge. Hence the central resistance 2R is ineffective.

Therefore the equivalent circuit is redrawn as follows.

$∴$ $\frac{1}{R_{P Q}} = \frac{1}{4 R} + \frac{1}{4 R} + \frac{1}{2 r} = \frac{r + r + 2 R}{4 R r}$

$∴$ $R_{P Q} = \frac{2 R r}{R + r}$

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