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:
Show Hint
- \( \frac{20}{3} \, \text{cm} \)
- \( \frac{40}{3} \, \text{cm} \)
- \( 100 \, \text{cm} \)
- \( \frac{50}{3} \, \text{cm} \)
The Correct Option is D
Solution and Explanation
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 \( \frac{50}{3} \, \text{cm} \).
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