Two wires A and B of the same material, having radii in the ratio 1: 2 and carry currents in the ratio 4: 1. The ratio of drift speed of electrons in A and B is

Question

Two wires A and B of the same material, having radii in the ratio 1: 2 and carry currents in the ratio 4: 1. The ratio of drift speed of electrons in A and B is (A) 16: 1 (B) 1: 16 (C) 1: 4 (D) 4: 1

Tardigrade Admin · Accepted Answer

Current flowing through the conductor, I= nevA. Hence (4/I)=(n e vd1 π(1)2/n e vd2 π(2)2) or (vd1/vd2)=(4 × 1/1)=(16/1)

Q. Two wires $A$ and $B$ of the same material, having radii in the ratio $1 : 2$ and carry currents in the ratio $4 : 1$ . The ratio of drift speed of electrons in $A$ and $B$ is

$16 : 1$

$1 : 16$

$1 : 4$

$4 : 1$

Current flowing through the conductor, $I = n e v A$ .
Hence $\frac{4}{I} = \frac{n e v _{d_{1}} π ( 1 ) ^{2}}{n e v _{d_{2}} π ( 2 ) ^{2}}$
or $\frac{v _{d_{1}}}{v _{d_{2}}} = \frac{4 \times 1}{1} = \frac{16}{1}$

Q. Two wires A and B of the same material, having radii in the ratio 1:2 and carry currents in the ratio 4:1. The ratio of drift speed of electrons in A and B is

16:1

1:16

1:4

4:1