Question

A piece of copper is to be shaped into a conducting wire of maximum resistance. The suitable length and diameter are __________ and __________ respectively.

• A. $L$ and $d$
• B. $2L$ and $d/2$
• C. $L/2$ and $2d$
• D. $2L$ and $d$

Answer 1

Answer: (B)

$2L$ and $d/2$

Resistance of copper wire $R=\rho \frac{L}{A}$

where $\rho$ is the resistivity of the material of wire and is constant.

Area of the wire $A=\frac{\pi d^2}{4}$

$⟹$ $R=k\frac{L}{d^2}$ where $k=\frac{\rho \pi }{4}=$ constant

(A) : $R_A=k\frac{L}{d^2}$

(B) : $R_B=k\frac{2L}{(d/2{)}^2}=8\frac{kL}{d^2}$

(C) : $R_C=k\frac{L/2}{(2d{)}^2}=\frac{1}{8}\frac{kL}{d^2}$

(D) : $R_D=k\frac{2L}{d^2}=2\frac{kL}{d^2}$

Hence dimensions of copper wire given in option B has the maximum resistance.