Question

Two wires each of radius of cross section $r$ but of different materials are connected together end to end (i.e., in series). If the densities of charge carriers in the two wires are in the ratio $2:3$, the drift velocity of electrons in the two wires will be in the ratio of

• A. $2:3$
• B. $3:2$
• C. $4:9$
• D. $9:4$

Answer 1

Answer: (B)

$3:2$

Let $n_1$ and $n_2$ be the densities of charge carriers in the two wires, $V_{d_1}$ and $V_{d_2}$ be the drift velocities of charge carriers in the two wires,
$A$ be the area of cross section,
$e$ is the charge on electron and
$I$ is the current flowing through both the wires
Hence, $I=n_{1}eA{V}_{d_1}=n_{1}eA{V}_{d_1}$
$\therefore n_1{V}_{d_1}=n_1{V}_{d_1}$

$\therefore \frac{V_{d_1}}{V_{d_2}}=\frac{n_2}{n_1}$

$\therefore \frac{V_{d_1}}{V_{d_2}}=\frac{3}{2}$