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 $\frac{4}{3}$ and $\frac{2}{3}$, then the ratio of the currents passing through the wires will be :

• A. $3$
• B. $\frac{1}{3}$
• C. $\frac{8}{9}$
• D. $2$

Answer 1

Answer: (B)

$\frac{1}{3}$

In this circuit two wires are connected in parallel, $i\propto 1/R$.
And resistance of wire of length $l$ and radius $r$ is given by,
$R=\frac{\rho l}{A}$, where, $\rho$ is the resistivity of the material.
So, $\frac{i_1}{i_2}=\frac{R_2}{R_1}=\frac{l_2}{l_1}\times \frac{A_1}{A_2}=\frac{3}{4}\times \frac{\pi {r_1}^2}{\pi {r_2}^2}$
$\Rightarrow \frac{i_1}{i_2}=\frac{3}{4}\times \frac{4}{9}=\frac{1}{3}$.