Question

Two wires of same material having lengths and radii in the ratio of $3:4$ and $3:2$ respectively are connected in parallel with a potential source of $6V$. The ratio of currents flowing through them, $I_1:I_2=$ _________.

• A. $3:1$
• B. $1:3$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is A $3:1$

We know that
$R_1=\rho \frac{I_1}{A_1}=\rho \frac{I_1}{\pi r_1^2}$
$R_2=\rho \frac{I_2}{\pi r_2^2}$
$\frac{R_1}{R_2}=\frac{I_1}{I_2}\times {\left(\frac{r_2}{r_1}\right)}^2$
$\frac{V/I_1}{V/I_2}=\frac{I_1}{I_2}\cdot {\left(\frac{r_2}{r_1}\right)}^2$ ($\because$ wire connected in parallel)
$\frac{I_2}{I_1}=\frac{3}{4}\times {\left(\frac{2}{3}\right)}^2$
$I_1:I_2=9\times 4:4\times 3$
$=3:1$