Question

Two wires each of radius of cross section $r$ but of different materials are connected together end to end (in series). If the densities of charge carriers in the two wires are in the ration $1:4$, the drift velocity of electrons in the two wires will be in the ratio:

• A. $2:1$
• B. $4:1$
• C. $1:2$
• D. $1:4$

Answer 1

Answer: (B)

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, $I=n_{1}eA{V}_{d_1}=n_{1}eA{V}_{d_2}$
$\therefore n_1{V}_{d_1}=n_2{V}_{d_2}$
$\therefore \frac{V_{d_1}}{V_{d_2}}=\frac{n_2}{n_1}$
$\therefore \frac{V_{d_1}}{V_{d_2}}=\frac{4}{1}$