Which expression represents the reactive power Q in an AC circuit with RMS voltage V_rms, RMS current I_rms, and phase angle φ between voltage and current?

Which expression represents the reactive power Q in an AC circuit with RMS voltage V_rms, RMS current I_rms, and phase angle φ between voltage and current?

• A. Q = V_rms I_rms sin φ
• B. P = I_rms V_rms cos φ
• C. S = V_rms I_rms
• D. p(t) instantaneous

Answer: (A)

In AC circuits, power has three components: real (useful work), reactive (energy stored and returned), and apparent (the overall power level). The reactive part depends on how out of phase the voltage and current are. Specifically, reactive power is the product of RMS voltage, RMS current, and the sine of the phase angle between them. So Q = V_rms I_rms sin φ. This contrasts with real power, which uses cos φ, and with apparent power, which is simply V_rms I_rms. The instantaneous power p(t) is v(t) i(t), a time-varying product, not the reactive component. That’s why the expression with sin φ correctly captures the reactive power.

In AC circuits, power has three components: real (useful work), reactive (energy stored and returned), and apparent (the overall power level). The reactive part depends on how out of phase the voltage and current are. Specifically, reactive power is the product of RMS voltage, RMS current, and the sine of the phase angle between them. So Q = V_rms I_rms sin φ. This contrasts with real power, which uses cos φ, and with apparent power, which is simply V_rms I_rms. The instantaneous power p(t) is v(t) i(t), a time-varying product, not the reactive component. That’s why the expression with sin φ correctly captures the reactive power.