Question

The voltage and current in a series AC circuit are given by V = V₀cos ωt and i = i₀ sin ωt. What is the power dissipated in the circuit?

Answer 1

Voltage, V = V₀cos ωt
Current, i = i₀ sin ωt or i = i₀ cos (ωt $-$ $\frac{\pi }{2}$)

Power dissipated in an AC circuit is given by,
$P=I_{rms}{V}_{rms}\cos \varphi$,
where I_rms = rms value of current
V_rms= rms value of voltage
ϕ = phase difference between current and voltage
Here, ϕ = $\pi$/2
$$\begin{gathered} \Rightarrow \cos \varphi =\cos \frac{\mathrm{\pi }}{2}=0 \\ \therefore P=I_{rms}{V}_{rms}\times 0=0 \end{gathered}$$