Question

Four resistances P, Q, R, X formed wheat stone bridge. The bridge is balanced when $R=64\Omega$. If P and Q are inter changed to bridge is balanced for $R=144\Omega$. The value of ‘X’ is

• A. $300\Omega$
• B. $200\Omega$
• C. $110\Omega$
• D. $96\Omega$

Answer 1

The correct option is D $96\Omega$

$\frac{P}{Q}=\frac{64}{X}\to \left(1\right)$
After interchange
$\frac{Q}{P}=\frac{144}{X}\to \left(2\right)\left(1\right)\times \left(2\right)gives\frac{P}{Q}\times \frac{Q}{P}=\frac{64\times 144}{X^2}X=\sqrt{64\times 144}=8\times 12X=96\Omega$