Two wires A and B of same material having their lengths in the ratio 6 : 1 are connected in series. The p.d. across the wires are 3V and 2V respectively. If rB and rB are radii of A and B respectively, the rB/rA is

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Two wires A and B of same material having their lengths in the ratio 6 : 1 are connected in series. The p.d. across the wires are 3V and 2V respectively. If r_Band r_Bare radii of A and B respectively, the $r_{B} / r_{A} is$

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answer is B.

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Detailed Solution

$I is same in series ρ is same for same material V = IR = I \frac{ρ l}{π r^{2}}; r^{2} \propto \frac{l}{V} \Rightarrow r \propto \sqrt{\frac{l}{V}} \frac{r_{B}}{r_{A}} = \sqrt{\frac{l_{B}}{l_{A}} \times \frac{V_{A}}{V_{B}}} = \sqrt{\frac{1}{6} \times \frac{3}{2}} = \frac{1}{2}$