Question

In a meter bridge a $30\Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left, the balance point is $37.5cm$ when $P$ and $Q$ are in series and $71.4cm$ when they are parallel. The values of $P$ and $Q$ (in $\Omega$ ) are

• A. 40; 10
• B. 35; 15
• C. 30; 20
• D. 25; 25

Answer 1

The correct option is C 30; 20

Case 1 Series

$\Rightarrow \frac{30}{P+Q}=\frac{37.5}{62.5}$

$\Rightarrow P+Q=50$

Case 2 Parallel

$\Rightarrow \frac{30}{\frac{PQ}{P+Q}}=\frac{71.4}{28.6}$

$PQ=\frac{30\times 50\times 28.6}{71.6}\approx 600$

$\Rightarrow Q=\frac{600}{P}$

$\Rightarrow P^2-50P+600=0$

$\Rightarrow (P-30)(P-20)=0$

$P=30\Omega$

$Q=20\Omega$