Question

A potential V is applied to a conductor of length L and diameter D , how are the electric field and drift velocity affected

(a.)when voltage is doubled

(b.)when length is doubled

(c)Diameter is doubled.

Answer 1

Using relations,
$$\begin{gathered} \mathrm{R}=\frac{\mathrm{\rho L}}{\mathrm{A}} \\ \mathrm{i}=\frac{\mathrm{V}}{\mathrm{R}} \\ \mathrm{i}={\mathrm{env}}_{\mathrm{drift}}.\mathrm{A} \\ \mathrm{And}\mathrm{E}=\mathrm{V}/\mathrm{L} \end{gathered}$$
(a) If the voltage is doubled while the resistance remains constant, the drift velocity and current will also double.
(b) If the length of the wire is doubled, its resistance also doubles and so the current in the wire will be reduced by a factor of two. Drift velocity is proportional to
current, so the drift velocity will be halved.
(c) If the wire’s diameter is doubled, the drift velocity remains the same. (Although, since there are more charge carriers, the current will quadruple.)
(a) E=V/L
For same length, if voltage is doubled, electric field will also be doubled.
(b) When length is doubled and voltage is constant, then E becomes half the original.
(c) Electric field in a uniform cross section is uniform with a magnitude E=V/L. Changing the diameter does not change the length of wire or voltage. Thus electric field is unchanged.