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A wire of resistance R, length l and uni...

A wire of resistance R, length l and uniform area of cross-section A is stretched till its length becomes double. It is then cut into three pieces of equal length which are connected in parallel. Find the net resistance of the combination in terms of the resistance R.

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To solve the problem step by step, we will follow these instructions: ### Step 1: Determine the new resistance after stretching the wire 1. **Initial Resistance**: The initial resistance of the wire is given as \( R \). 2. **Initial Length and Area**: The initial length of the wire is \( l \) and the area of cross-section is \( A \). 3. **New Length**: When the wire is stretched to double its length, the new length \( l' = 2l \). 4. **Volume Conservation**: The volume of the wire remains constant before and after stretching. Therefore, we have: ...
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Knowledge Check

  • A uniform wire of resistance r is cut into n parts and they are connected in parallel. Effective resistance of the combination is

    A
    `( r )/(n )`
    B
    `( r )/( n^(2))`
    C
    `rn `
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    A
    nR
    B
    `(R)/(n)`
    C
    `(n)/(R)`
    D
    `(R)/(n^(2))`

  • A wire of resistance R is cut into n equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be

    A
    nR
    B
    `(R)/(n)`
    C
    `(n)/(R)`
    D
    `(R)/(n^(2))`

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