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Question

If a wire of resistance R is stretched to double of its length, then new resistance will be :


A
R/2
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B
2 R
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C
4 R
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D
16 R
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Solution

The correct option is C 4 R

$$\textbf{Step 1: Finding the new cross section Area of the wire}$$

Volume of wire remains constant even after stretching the wire.

$$V_i= V_f$$

$$\Rightarrow LA= L' A'$$  ( given $$L'=2L$$)

$$\Rightarrow A'= \dfrac{A}{2}$$

$$\textbf{Step 2: Finding the New Resistance}$$

Initial resistance, $$ R = \dfrac{\rho L}{A}$$

New resistance, $$ R' = \displaystyle \dfrac{\rho L'}{A'} = \dfrac{\rho (2L)}{\dfrac{A}{2}} =\dfrac{4 \rho L}{A} =4R$$

Hence, Option C is correct

Physics

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