Question

Two conducting wires A and B are made of same material. If the length of B is twice that of A and the radius of circular cross-section of A is twice that of B, then their resistances $R_A$ and $R_B$ are in the ratio __________.

• A. $2:1$
• B. $1:2$
• C. $1:8$
• D. $1:4$

Answer 1

The correct option is C $1:8$

We know that.

$R=$ $\rho$$\frac{l}{A}$

Thus $R\propto$ $l$ and $R\propto$ $\frac{1}{A}$

$\frac{R_A}{R_B}$ = $\frac{l_A}{l_B}\times$$\frac{A_B}{A_A}$

$\therefore$ $\frac{R_A}{R_B}$ = $\frac{l_A}{2l_A}\times$$\frac{\pi r_B^2}{\pi r_A^2}$

$\therefore$ $\frac{R_A}{R_B}$ = $\frac{l_A}{2l_A}\times$$\frac{\pi r_B^2}{\pi 2^2{r}_B^2}$

$\therefore$ $\frac{R_A}{R_B}$ = $\frac{1}{2}\times$$\frac{1}{4}$ = $\frac{1}{8}$