(II) In the LRC circuit or Fig. 30–19, suppose I = I0 sin ωt and V − V0 sin(ωt + ϕ). Determine the instantaneous power dissipated in the circuit from P = IV using these equations and show that on the average,
FIGURE 30-19 An LRC circuit.
We multiply the instantaneous current by the instantaneous voltage to calculate the instantaneous power. Then using the trigonometric identity for the summation of sine arguments (inside back cover of text) we can simplify the result. We integrate the power over a full period and divide the result by the period to calculate the average power.
P = IV = (I0 sin ωt)V0 sin(ωt + ϕ) = I0V0 sin ωt cosϕ +sinϕ cos ωt)
= I0V0 (sin2 ωt cosϕ +sin ωt cos ωt sinϕ
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