Question

A copper rod of cross-sectional area $A$ carries a uniform current $I$ through it. At temperature $T$, if the volume charge density of the rod is $\rho$, how long will the charges take to travel a distance $d$ ?

• A. $\frac{2 \, \rho \, d \, A}{I}$
• B. $\frac{2 \, \rho \, d \, A}{I \, T }$
• C. $\frac{ \rho \, d \, A}{I }$
• D. $\frac{ \rho \, d \, A}{I \, T }$

Answer 1

Answer: (C)

Given: Volume charge density of rod $=\rho$.
We know that current $I=n e A v ;$
where $n$ is number of electrons, $e$ is electronic charge, $A$ is area, $v_{ d }$ is drift velocity

Since volume charge density is $\rho= ne$ . Therefore,
Now, time $=\frac{\text { distance }}{\text { speed }} $
$\Rightarrow \text { time }=\frac{d}{V_{d}}=\frac{d}{I / \rho A}=\frac{\rho A d}{I}$
Thus, time required to travel distance $d=\frac{\rho d A}{I}$