Which formula describes the power in a resistive AC circuit in terms of RMS voltage and resistance?

Which formula describes the power in a resistive AC circuit in terms of RMS voltage and resistance?

• A. V_rms^2 / R
• B. V_peak^2 / R
• C. V_rms × I_rms
• D. V_peak × I_peak

Answer: (A)

In a resistive AC circuit, the instantaneous power is p(t) = v(t) i(t). Since a resistor has i(t) = v(t)/R, this becomes p(t) = v^2(t)/R. The average (real) power over time is P = V_rms^2 / R, because V_rms is the effective voltage that accounts for heating in the resistor. This form directly uses RMS voltage and resistance, which is why it’s the correct expression for power in this context. While P can also be written as V_rms I_rms in a purely resistive circuit (since I_rms = V_rms / R), the formula that explicitly involves RMS voltage and resistance is V_rms^2 / R. Using peak values would not reflect the average power delivered.

In a resistive AC circuit, the instantaneous power is p(t) = v(t) i(t). Since a resistor has i(t) = v(t)/R, this becomes p(t) = v^2(t)/R. The average (real) power over time is P = V_rms^2 / R, because V_rms is the effective voltage that accounts for heating in the resistor. This form directly uses RMS voltage and resistance, which is why it’s the correct expression for power in this context. While P can also be written as V_rms I_rms in a purely resistive circuit (since I_rms = V_rms / R), the formula that explicitly involves RMS voltage and resistance is V_rms^2 / R. Using peak values would not reflect the average power delivered.