Question

In the circuit shown in figure, what will be the effective resistance between points A and B ?
(A) r
(B) r/2
(C) r/3
(D) 2r

Answer 1

resistor CD can be removed because PQRS follows ideal WEATSONE BRIDGE .

so, $R_{QR}=R+R=2R$
similarly, $R_{PS}=R+R=2R$
now, $R_{QR}$ and $R_{PS}$ are in parallel combination.
so, R' = $\frac{R_{QR}\times R_{PS}}{R_{QR}+R_{PS}}$

R' = 2R × 2R/(2R + 2R) = R

now, R' and $R_{AB}$ are in parallel combination.
so, Req = R × R/(R + R) = R/2

hence, option (B) is correct.