Meter Bridge

The correct answer is 40
Even if the radius of wire is doubled, the balancing point would not change as

, which is not including a term of area.
Therefore , balancing length will be 40 cm

In this problem, we need to find the change in the balance length of a meter bridge when an unknown resistance is shunted with a known resistance. Let's solve this step-by-step:

A meter bridge works on the principle of a balanced Wheatstone bridge, where the balance condition is given by:

1. The balance condition:

1. Where is the resistance in the left gap, is the resistance in the right gap, and and are the lengths of the bridge wire.

Initially, a resistance of is placed in the left gap, and the unknown resistance is in the right gap, with a balance length .

1. We can express the balance condition as:

Solving for , we have:

1. Rearranging yields:

Now, the unknown resistance is shunted with a resistor. When resistors are shunted (connected in parallel), the effective resistance is given by:

1. Formula for parallel resistances:

Substituting :

1. Calculate :

With the new effective resistance, the balance length can be recalculated using the new balance condition:

1. Recalculate the balance condition:

Substituting , we get:

1. Calculate :

Solve for :

Hence, the change in the balance length is:

Therefore, the balance length changes by 22.5 cm, which matches the given correct answer.

Given:

Step 1: Equation for the resistors

Step 2: Solving the system of equations

From equations (i) and (ii), we get:

Final Answer: