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. 403.5 ohm
• B. 404.5 ohm
• C. 401.5 ohm
• D. 402.5 ohm

Answer 1

Answer: (D)

Initiality
$\frac{ P }{ Q }=\frac{ R _{1}}{ X }$
After interchanging $P$ and $Q$
$\frac{ Q }{ P }=\frac{ R _{2}}{ X }$
From (1) and (2)
$1=\frac{ R _{1} \times R _{2}}{ X ^{2}} $
$X =\sqrt{ R _{1} R _{2}}$
$X =\sqrt{400 \times 405}=402.5 \Omega$