Question

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

• A. $\frac{2Rr}{(R+r)}$
• B. $8R\frac{(R+r)}{(3R+r)}$
• C. 2r + 4R
• D. $\frac{5R}{2+2r}$

Answer 1

The correct option is A $\frac{2Rr}{(R+r)}$

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
$\frac{1}{R_e}=\frac{1}{4R}+\frac{1}{2r}+\frac{1}{4R}$
which gives $R_e=\frac{2Rr}{(R+r)}$