1. Use the relation between current and drift velocity

For a conductor carrying current, the current is $I = \rho \, A \, v_d$ where:

• $\rho$ = volume charge density,
• $A$ = cross-sectional area,
• $v_d$ = drift speed of charges.

This follows because in time $dt$, charge crossing a section is $dq = \rho \,(A\,v_d\,dt)$ so $I = \frac{dq}{dt} = \rho A v_d.$

2. Find the drift speed

From $I = \rho A v_d,$ we get $v_d = \frac{I}{\rho A}.$

3. Time taken to travel distance $d$

If the changes/charge drift travel distance $d$ with speed $v_d$, then $t = \frac{d}{v_d} = \frac{d}{I/(\rho A)}.$

Thus, $t = \frac{\rho d A}{I}.$

4. Match with the options

This corresponds to: $\boxed{\frac{\rho d A}{I}}$ which is Option C.

5. About temperature $T$

Although temperature is mentioned, it does not appear in the required expression because the time depends directly on drift velocity, and with given $I, \rho,$ and $A$, the result is independent of $T$.