Two wires A and B, of the same material having lengths in the ratio \( 1:2 \) and diameters in the ratio \( 2:3 \) are connected in series with a battery. The ratio \( (V_A/V_B) \) of the potential differences across the two wires is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 9/8 \)
Wires of the same material have \( R = \rho l/A \) with \( A = \pi d^{2}/4 \), so \( R \propto l/d^{2} \). In series the same current flows through both, so the potential difference is proportional to resistance.
\( \displaystyle \frac{V_A}{V_B} = \frac{R_A}{R_B} = \frac{l_A}{l_B}\times\left(\frac{d_B}{d_A}\right)^{2} \)
\( \displaystyle \frac{V_A}{V_B} = \frac{1}{2}\times\left(\frac{3}{2}\right)^{2} = \frac{1}{2}\times\frac{9}{4} = \frac{9}{8} \)