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

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

The Effective Resistance Between Points P And Q Of The Elect...

Options:

A . 2Rr(R+r)

B . 8R(R+r)(3R+r)

C . 2r + 4R

D . 5R2+2r

Answer: Option A
:
A

The Effective Resistance Between Points P And Q Of The Elect...

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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