CAIE A-Level Physics A2 21.1.4 Root Mean Square R M S and Peak Values and Recall and Use I R M S I0

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An electron in a metal rod moves randomly about a mean position. When an alternating voltage is applied to the ends of the rod, the mean position can be considered to oscillate with simple harmonic motion along the axis of the rod. Fig. 4.1 shows the variation with time t of the displacement x of the mean position from a fixed point on the axis of the rod.

Fig. 4.1

The rod has a cross-sectional area of $4.3 \mathrm{~cm}^{2}$ and contains a number density of conduction electrons (charge carriers) of $8.5 \times 10^{28} \mathrm{~m}^{-3}$ .

All of the conduction electrons in the rod may be assumed to be oscillating in phase with, and with the same amplitude as, the oscillation shown in Fig. 4.1.

Determine the root-mean-square (r.m.s.) current in the rod.
r.m.s. current = A

$\begin{aligned} I_{\text {r.m.s. }} =I_{0} / \sqrt{ } 2 =0.64 / \sqrt{ } 2 =0.45 \mathrm{~A} \end{aligned}$

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CAIE A-Level Physics A2 21.1.4 Root Mean Square R M S and Peak Values and Recall and Use I R M S I0 Topic Practice

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