The effective resistance between points P and Q of the electrical circuit shown

Discussion Forum : Current Electricity

Question -

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

Options:

A .

\frac{2 R r}{(R + r)}

B .

8 R \frac{(R + r)}{(3 R + r)}

C . 2r + 4R

D .

\frac{5 R}{2 + 2 r}

Answer: Option A
:
A

The branches ABPQ and PQCD are a balanced Wheatstone's bridge. Therefore resistances between E and E and between F and G do not contribute and the circuit simplies to the one show in figure. The effective resistance $R_{e}$ between P and Q is given by
$\frac{1}{R_{e}} = \frac{1}{4 R} + \frac{1}{2 r} + \frac{1}{4 R}$
which gives $R_{e} = \frac{2 R r}{(R + r)}$

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