Question

Current is flowing through a conductor of non-uniform cross-section. If $A_1>A_2$, then the relation between the drift velocity $\left(V\right)$ and current at the two cross- sections respectively, will be

• A. $V_1>V_2$ and $i_1>i_2$
• B. $V_1<V_2$ and $i_1=i_2$
• C. $V_1<V_2$ and $i_1<i_2$
• D. $V_1=V_2$ and $i_1=i_2$

Answer 1

The correct option is B $V_1<V_2$ and $i_1=i_2$


Given: $A_1>A_2$

According to the conservation of charge principle, charge crossing through any cross-section per unit time will be equal.

$\Rightarrow i_1=i_2=i$

Now current density, $J=\frac{i}{A}$

Thus, $J_1=\frac{i}{A_1}$ & $J_2=\frac{i}{A_2}$

$(\because A_1>A_2)$

$\therefore J_1<J_2$

From the relation of drift speed,
$V_d=\frac{J}{ne}$

$\Rightarrow V_d\propto J$

Hence, $V_1<V_2$

Hence, $\left(B\right)$ is the correct answer.