Question

In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When $R=400\Omega$, the bridge is equal. When $R=400\Omega$,the bridge is balanced. On inter-changing $P$ and $Q$, the value of $R$, for balance, is$405\Omega$.
The value of X is close to :

• A. $403ohm$
• B. $404.5ohm$
• C. $401.5ohm$
• D. $402.5ohm$

Answer 1

The correct option is D $402.5ohm$

Initiality

$\frac{P}{Q}=\frac{R_1}{X}$____(1)

After interchanging P and Q

$\frac{Q}{P}=\frac{R_2}{X}$_____(2)

From (1) and (2)

$1=\frac{R_1\times R_2}{X^2}$

$X=\sqrt{R_1{R}_2}$

$X=\sqrt{400\times 405}=402.5\Omega$