Question

An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the lengths and radii of the wires are in the ratio of $4/3$ and $2/3$ respectively, then the ratio of the currents passing through the wires will be -

• A. $1/3$
• B. $1/5$
• C. $8/9$
• D. $2$

Answer 1

The correct option is A $1/3$

Since wires are connected in parallel, the potential difference across the wires will be the same.

$I_1=\frac{V}{R_1}$ and $I_2=\frac{V}{R_2}$

$\Rightarrow \frac{I_1}{I_2}=\frac{R_2}{R_1}$

Here,

$R_1=\rho \frac{l_1}{A_1}=\rho \frac{l_1}{\pi r_1^2}$, and

$R_2=\rho \frac{l_2}{\pi r_2^2}$

$\Rightarrow \frac{I_1}{I_2}=\frac{\rho \frac{l_2}{\pi r_2^2}}{\rho \frac{l_1}{\pi r_1^2}}=\frac{l_2{r}_1^2}{l_1{r}_2^2}$

$\Rightarrow \frac{I_1}{I_2}=\frac{3}{4}\times {\left(\frac{2}{3}\right)}^2=\frac{1}{3}$

Hence, option $\left(A\right)$ is the correct answer.