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Meter bridge balance length when the bridge wire is replaced

This type of question, asked 2 times: 27 Jul 2022, 31 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    27 Jul 2022

    112
    In the given figure of meter bridge experiment, the balancing length ACAC corresponding to null deflection of the galvanometer is 40 cm40\text{ }cm. The balancing length, if the radius of the wire ABAB is doubled, will be ____\_\_\_\_ cm.

  2. Question 2

    31 Jan 2024

    99
    The resistance per centimeter of a meter bridge wire is rr, with XΩX\Omega resistance in left gap. Balancing length from left end is at 40 cm40\text{ }cm with 25Ω25\Omega resistance in right gap. Now the wire is replaced by another wire of 2r2r resistance per centimeter. The new balancing length for same settings will be at

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