Wire $A$ is twice as long as wire $B$ but is otherwise identical. The electric field acting in each has the same magnitude. How do the currents flowing in these wires compare?
A) $I_{A}=4 I_{B}$
B) $I_{A}=2 I_{B}$
C) $I_{A}=I_{B}$
D) $I_{A}=(1 / 2) I_{B}$
E) $I_{A}=(1 / 4) I_{B}$
F) Other (specify)
G) It is impossible to say given the provided information.

Question

Quizplus · Accepted Answer

The current $I$ flowing through a wire in an electric field is determined by the equation $I = nAve$, where $n$ is the charge carrier density, $A$ is the cross-sectional area, $v$ is the drift velocity, and $e$ is the charge of an electron. Since both wires are identical except for their length and are subjected to the same electric field, the drift velocity $v$ induced in them will be the same. The cross-sectional area $A$ and material properties (which affect $n$ and $e$) are also the same. Therefore, the currents $I_{A}$ and $I_{B}$ will be equal, as the length of the wire does not directly affect the current in this context.

Wire AAA Is Twice as Long as Wire BBB But Is Otherwise Identical

Wire $A$ Is Twice as Long as Wire $B$ But Is Otherwise Identical