A long straight copper wire of cross-sectional area carries an alternating current…

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

A long straight copper wire of cross-sectional area

A

carries an alternating current described by

I(t)=I_{0}\cos(\omega t),

with

I_{0}=5.0\,\text{A}

and angular frequency

\omega=2\pi\times120\,\text{rad}\,\text{s}^{-1}

. The number density of free electrons is

n=8.5\times10^{28}\,\text{m}^{-3}

. (a) Derive an expression for the instantaneous drift velocity

v_{d}(t)

of the electrons in terms of the given quantities. (b) Integrate

v_{d}(t)

over one complete cycle to determine the net displacement of an individual electron after one full period. (c) Compute the root-mean-square (rms) value of the drift velocity for this wire. (d) Discuss how your results in parts (b) and (c) reconcile the microscopic motion of charge carriers with the macroscopic measurement of zero average current over a cycle.

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