The resistance of a wire is . Its new resistance in ohm, if stretched to 5 times of its original length, will be [2023]

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Solution

Q.
The resistance of a wire is $5 Ω$ . Its new resistance in ohm, if stretched to 5 times of its original length, will be [2023]

1 125

2 5

3 25

4 625

Ans.
(1)

$∴$ $Volume of wire is constant in stretching$

$V_{i} = V_{f}$

$A_{i} l_{i} = A_{f} l_{f}$

$A l = A' (5 l)$

$A' = \frac{A}{5}$

$R_{f} = \frac{ρ l_{f}}{A_{f}} = \frac{ρ (5 l)}{(\frac{A}{5})} = 25 (\frac{ρ l}{A}) = 25 \times 5 = 125 Ω$

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