Question

Two unknown resistances X and Y are connected in left and right gaps of a metre bridge and the balancing point is obtained at 50 cm from left. When a $20\Omega$ resistance is connected in series with X, the balancing point is at 60 cm from left. The values of X and Y respectively (in ohms) are

• A. 40, 10
• B. 40, 20
• C. 20, 20
• D. 40, 40

Answer 1

The correct option is D

40, 40

Initially when the balancing point is at 50 cm from left, $\frac{X}{Y}=\frac{l}{100-l}\Rightarrow \frac{X}{Y}=\frac{50}{100-50}\Rightarrow X=Y$
Now, when $20\Omega$ resistance is conneceted in series with X, $\frac{X+20}{Y}=\frac{l_1}{100-l_1}\Rightarrow \frac{X+20}{X}=\frac{60}{100-60}=\frac{3}{2}\therefore X=Y=40\Omega$