Question

In a metre bridge, the gaps are closed by two resistances P and Q and the balance point is obtained at 40 cm. When Q is shunted by a resistance of 10$\Omega$, the balance point shifts to 50cm, The values of P and Q arc

• A. $\frac{10}{3}\Omega ,5\Omega$
• B. $20\Omega$, 30$\Omega$
• C. $10\Omega$, 15$\Omega$
• D. $5\Omega$ ,$\frac{15}{2}\Omega$

Answer 1

The correct option is A $\frac{10}{3}\Omega ,5\Omega$

Balanced condition of meter bridge in 1 st case : $\frac{P}{Q}=\frac{40}{100-40}=\frac{2}{3}.....\left(1\right)$

When Q is shunted , it means a resistance $10\Omega$ is connected in

parallel across Q. so Q arm becomes $\frac{10Q}{Q+10}$

so now balanced condition : $\frac{P(Q+10)}{10Q}=\frac{50}{100-50}$

or $P/10+P/Q=1$

using (1), $P/10+2/3=1$ or $P=\frac{10}{3}\Omega$

now $Q=\left(3/2\right)P=\left(3/2\right)\left(10/3\right)=5\Omega$