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, $V=i_1{R}_1=i_2{R}_2$
$\Rightarrow \frac{i_1}{i_2}=\frac{R_2}{R_1}=\frac{32}{1}$.