Question

A cylindrical rod is reformed to twice its length with no change in its volume. If the resistance of the rod was R, the new resistance will be

• A. $R$
• B. $2R$
• C. $4R$
• D. $8R$

Answer 1

Answer: (C)

$4R$

Volume $=\pi r^{2}L=A\times L$

$L^{\prime }=2L$

$⟹A^{\prime }=\frac{A}{2}$ Since volume is constant.

We know,

R $=\frac{\rho \times L}{A}$

Hence,

$\frac{R^{\prime }}{R}=\frac{L^{\prime }}{L}\times \frac{A}{A^{\prime }}=\frac{2L}{L}\times \frac{A}{\frac{A}{2}}=4$

Hence,

$R^{\prime }=4R$