Question

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

• A. $401.5\Omega$
• B. $404.5\Omega$
• C. $403.5\Omega$
• D. $402.5\Omega$

Answer 1

The correct option is D $402.5\Omega$

Using Wheatstone bridge balance condition in first case,

$\frac{P}{Q}=\frac{R}{X}---\left(1\right)$

Using Wheatstone bridge balance condition after interchanging,

$\frac{Q}{P}=\frac{R^{\prime }}{X}$

$\Rightarrow \frac{P}{Q}=\frac{X}{R^{\prime }}---\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,

$\frac{R}{X}=\frac{X}{R^{\prime }}$

$\Rightarrow X^2=R{R}^{\prime }=400\times 405$

$\Rightarrow X=402.5\Omega$

Hence, option $\left(D\right)$ is correct.