Question

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

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

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 correctPhysics

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