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

$\Rightarrow \frac{v_p}{v_Q}={\left(\frac{d_Q}{d_p}\right)}^2={\left(\frac{d/2}{d}\right)}^2=\frac{1}{4}\Rightarrow v_p=\frac{1}{4}{v}_Q.$