Answer to Question #88479 in Electric Circuits for Sridhar

Question

In a meter bridge experiment, when a nichrome wire is in the right gap, the balancing length is 60cm. When the nichrome wire is uniformly stretched to increase its length by 20% and again connected in the right gap, the new balancing length is nearly.
Ans 51cm

Answer 1

For the first situation we can simply write the equation of the meter bridge for the left and right sides:

$$R_L/R_R=\frac{60}{100-60}=1.5.$$

When the took the nichrome wire, stretched it and connected again, its normal area $A$ on the right side decreases (since the metal wire has constant volume) by factor of 1.2:

$$V=Al=A_\text{stretched}\cdot1.2l,$$

$$A_\text{stretched}=A/1.2.$$

This affects the resistance in the right side:

$$R_{R\text{stretched}}=\rho\frac{1.2l}{A/1.2}=1.44\rho\frac{l}{A}=1.44R_R.$$

For the stretched wire case we have:

$$\frac{R_L}{1.44R_R}=\frac{1.5}{1.44}=\frac{x}{100-x},$$

$$x=51.02\text{ cm}.$$