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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?
Solution
Voltage, V = V0cos ωt
Current, i = i0 sin ωt or i = i0 cos (`wt - pi/2`)
Power dissipated in an AC circuit is given by,
`P = I_rms V_rms cos Ø`,
where Irms = rms value of current
Vrms= rms value of voltage
ϕ = phase difference between current and voltage
Here, ϕ = `pi`/2
⇒ `cos Ø = cos pi/2 = 0`
∴` P = Irms Vrms xx o = 0`
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