Question

A current I is passing through a wire having two sections P and Q of uniform diameters d and $\frac{d}{2}$ respectively. If the mean drift velocity of electrons in section P and Q is denoted by $v_p$ and $v_q$ respectively, then

• A. $v_p=v_q$
• B. $v_p=\frac{1}{2}{v}_q$
• C. $v_p=\frac{1}{4}{v}_q$
• D. $v_p=2v_q$

Answer 1

The correct option is C $v_p=\frac{1}{4}{v}_q$

Drift velocity $v_d=\frac{i}{neA}\Rightarrow v_d\propto \frac{1}{A}or{v}_d\propto \frac{1}{d^2}$

$\Rightarrow \frac{v_p}{v_q}={\left(\frac{d_q}{d_p}\right)}^2={\left(\frac{\frac{d}{2}}{d}\right)}^2=\frac{1}{4}\Rightarrow v_p=\frac{1}{4}{v}_q$