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 speeds of electrons in A and B is:

• A. 16 : 1
• B. 1 : 16
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is A 16 : 1

Current is given by $i=neA{v}_d$, where
n = no. of electrons,
$e$ = electron charge,
$A$ = cross-sectional area of the conductor and
$v_d$ = drift velocity of electrons.
Since, $n$ and $e$ are constant:
$\frac{i_1}{i_2}=\frac{A_1}{A_2}\times \frac{v_{d_1}}{v_{d_2}}$,
$\Rightarrow$$\frac{i_1}{i_2}=\frac{r_1^2}{r_2^2}\times \frac{v_{d_1}}{v_{d_2}}$
$⟹\frac{4}{1}=\frac{1^2}{2^2}\times \frac{v_{d_1}}{v_{d_2}}$
$⟹\frac{v_{d_1}}{v_{d_2}}=\frac{4\times 4}{1\times 1}=16:1$.