An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of two wires are in the ratio of 4 : 3 and 2 : 3 respectively, the ratio of the currents in the wires will respectively be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 3
Wires in parallel have the same potential difference across them, so the current in each is inversely proportional to its resistance, \( I = V/R \). For wires of the same material, \( R = \rho l/(\pi r^{2}) \).
\( \displaystyle \frac{R_1}{R_2} = \frac{l_1}{l_2}\times\frac{r_2^{2}}{r_1^{2}} = \frac{4}{3}\times\frac{3^{2}}{2^{2}} = \frac{4}{3}\times\frac{9}{4} = 3 \)
\( \displaystyle \frac{I_1}{I_2} = \frac{R_2}{R_1} = \frac{1}{3} \)