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

Answer 1

The correct option is C 4 R

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

Volume of wire remains constant even after stretching the wire.

$V_i=V_f$

$\Rightarrow LA=L^{\prime }{A}^{\prime }$ ( given $L^{\prime }=2L$)

$\Rightarrow A^{\prime }=\frac{A}{2}$

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

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

New resistance, $R^{\prime }=\frac{\rho L^{\prime }}{A^{\prime }}=\frac{\rho \left(2L\right)}{\frac{A}{2}}=\frac{4\rho L}{A}=4R$

Hence, Option C is correct