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 $\frac{1}{2}$ and $\frac{4}{1},$ then the ratio of the currents passing through the wires will be

• A. 8 / 9
• B. 32 / 1
• C. 3
• D. 2

Answer 1

Answer: (B)

$R_{1}=\frac{\rho l_{1}}{\pi r_{1}^{2}}, R_{2}=\frac{\rho l_{2}}{\pi r_{2}^{2}}$
$\frac{R_{1}}{R_{2}}=\left(\frac{l_{1}}{l_{2}}\right) \cdot\left(\frac{r_{2}}{r_{1}}\right)^{2}$
$=\left(\frac{1}{2}\right)\left(\frac{1}{4}\right)^{2}=\frac{1}{32}$
Now, $V=i_{1} R_{1}=i_{2} R_{2}$
$\Rightarrow \frac{i_{1}}{i_{2}}=\frac{R_{2}}{R_{1}}=\frac{32}{1}$.