In an AC circuit with R, L, and C, the average power P is P = V_rms I_rms cos φ. Which statement is true for a purely resistive load?

• A. P = V_rms I_rms
• B. P = I_rms^2 R
• C. P = V_rms^2 / R
• D. P = (V_rms I_rms)^2 / R

Answer: (C)

For a purely resistive load, voltage and current are in phase, so the power factor is 1 and the average power becomes P = V_rms I_rms. Using Ohm’s law for a resistor, V_rms = I_rms R, which gives P = I_rms^2 R. This is equivalent to P = V_rms^2 / R, which expresses the power directly in terms of the voltage across the resistor and its resistance. That form is a common and convenient way to represent the power for a pure resistor, hence it is the true statement here.