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. $\frac{2\rho dA}{I}$
• B. $\frac{2\rho dA}{IT}$
• C. $\frac{\rho dA}{I}$
• D. $\frac{\rho dA}{IT}$

Answer 1

Answer: (C)

Given: Volume charge density of rod $=\rho$.
We know that current $I=neAv;$
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 $=\frac{\text{ distance }}{\text{ speed }}$
$\Rightarrow \text{ time }=\frac{d}{V_d}=\frac{d}{I/\rho A}=\frac{\rho Ad}{I}$
Thus, time required to travel distance $d=\frac{\rho dA}{I}$