Question

In a metre-bridge when a resistance in the left gap is 2Ω and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with 2Ω, the balance length changes by : 

(1) 22.5 cm 

(2) 20 cm 

(3) 62.5 cm 

(4) 65 cm

Answer 1

(1) 22.5 cm 

First case \(\frac {2}{40} = \frac {X}{60} \Rightarrow X = 3 \Omega\)

In second case \(X' = \frac {2 \times 3}{2+ 3} = 1.2 \Omega\)

\(\frac {2}{l}=\frac {1.2}{100-l}\)

200 - 2l = 1.2l

\(l= \frac {200}{3.2} = 62.5 \,cm\)

Balance length changes by 22.5 cm