In an ac circuit, the emf (ε) and the current (i) at any instant are given respectively by ε=E₀ sin ω t and i=I₀ sin (ω t-φ). The average power in the circuit over one cycle of ac is

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(1) (E₀I₀)/2 cos φ. Average the instantaneous product over a cycle: P= E₀ sin ω t· I₀ sin (ω t-φ). Expanding the second sine and using sin²ω t=1/2 and sin ω t cos ω t=0 gives P=(E₀I₀)/2 cos φ. In rms terms this is the familiar P=EᵣₘₛIᵣₘₛ cos φ, since each rms value carries a 1/(√2).

In an ac circuit, the emf (ε) and the current (i) at any instant are given respectively by ε=E₀ sin ω t and i=I₀ sin (ω t-φ). The average power in the circuit over one cycle of ac is

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