Question

In given figure of wheatstone bridge , 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 $405\Omega$ . Choose the closest value of $X$ from the following option :

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

Answer 1

Answer: (B)

Initially $\frac{P}{Q}=\frac{R_1}{x}$
After interchanging $P$ and $Q$ are $\frac{Q}{P}=\frac{R_2}{x}$ ____(2)
From $\left(\right.i\left.\right)$ and $\left(\right.ii\left.\right)$
$1=\frac{R_{1} R_{1}}{x^{2}}$
$x=\sqrt{R , R_{2}}$
$=\sqrt{400 \times 405}$
$=402.5\Omega$