Power for a resistor (18-24)

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Question

Resistance of the resistor

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Review

Figure 21-2 graphs the voltage $V(t)$ as a function of time. The angular frequency $\omega$ of the voltage (in rad/s) is related to the frequency $f$ of the voltage (in Hz) by the same relationship we used in Section 12-3 for simple harmonic motion:

$\omega = 2\pi{f}$

The period $T$ of the oscillation is equal to $1/f$ . For example, in the United States and Canada ac voltage is applied at a frequency $f = 60\ \mathrm{Hz}$ , so the period of oscillation is $T = 1/f = 1/ (60\ \mathrm{Hz})= 0.017 \mathrm{s}$ and the angular frequency is $\omega = 2\pi{f} = (2\pi\mathrm{rad})\ (60\ \mathrm{Hz}) = 3.8 \times 10^2\ \mathrm{rad}/s$ .

If we attach a source of ac voltage described by Equation 21-1 to a resistor of resistance $R$ , we can still use Equation 18-24 to calculate the power that flows into the resistor: