JEE MAIN - Physics (2018 - 15th April Evening Slot - No. 15)
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 changes take to travel a distance d ?
$${{2\rho \,d\,A} \over {\rm I}}$$
$${{2\rho \,d\,A} \over {{\rm I}\,T}}$$
$${{\rho \,d\,A} \over {{\rm I}\,}}$$
$${{\rho \,d\,A} \over {{\rm I}\,T}}$$
Explanation
Given : Volume charge density of rod = $$\rho$$.
We know that current $$I = neA{v_d}$$; where n is number of electrons, e is electronic charge, A is area, vd is drift velocity
_15th_April_Evening_Slot_en_15_1.png)
Since volume charge density is $$\rho$$ = ne. Therefore,
$$I = \rho A{v_d} \Rightarrow {v_d} = {I \over {{\rho _A}}}$$
Now, time = $${{dis\tan ce} \over {speed}}$$
$$\Rightarrow$$ time $$ = {d \over {{v_d}}} = {d \over {I/\rho A}} = {{\rho Ad} \over I}$$
Thus, time required to travel distance $$d = {{\rho dA} \over I}$$
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