Question

Two equal resistances are connected in the two gaps of a meter bridge. If the resistance in the right gap is doubled, then the change in the balancing length is:

• A. \( \frac{20}{3} \, \text{cm} \)
• B. \( \frac{40}{3} \, \text{cm} \)
• C. \( 100 \, \text{cm} \)
• D. \( \frac{50}{3} \, \text{cm} \)

Hint:

In a meter bridge, the balancing length is inversely proportional to the resistance in the right gap.

Answer 1

The Correct Option is D

Step 1: In a meter bridge, the balance length \( l \) is given by the formula: \[ \frac{l}{100 - l} = \frac{R_2}{R_1} \] where \( R_1 \) and \( R_2 \) are the resistances in the two gaps. 

Step 2: If the resistance in the right gap is doubled, the new balance length is adjusted. 

Step 3: The change in the balancing length is found to be \( \frac{50}{3} \, \text{cm} \).