What term describes the value of a sine-wave alternating current needed to produce the same amount of heat as direct current?

What term describes the value of a sine-wave alternating current needed to produce the same amount of heat as direct current?

• A. Peak Voltage
• B. Inductance
• C. Capacitance
• D. Effective Value

Answer: (D)

Heat in a resistor from AC depends on the average of the square of the current: P = I^2R. For a sine-wave current i(t) = I_peak sin(ωt), the average of i^2 over a cycle is I_peak^2/2, so the heating effect corresponds to I_rms^2 R, where I_rms = I_peak/√2. This RMS, or effective, value is the DC-equivalent current that would produce the same heat in the resistor. The same idea applies to voltage: V_rms = V_peak/√2, and P = V_rms^2/R. Inductance and capacitance describe reactive energy storage, not the steady heating effect. So the term describing the heating-equivalent value is the effective (RMS) value.

Heat in a resistor from AC depends on the average of the square of the current: P = I^2R. For a sine-wave current i(t) = I_peak sin(ωt), the average of i^2 over a cycle is I_peak^2/2, so the heating effect corresponds to I_rms^2 R, where I_rms = I_peak/√2. This RMS, or effective, value is the DC-equivalent current that would produce the same heat in the resistor. The same idea applies to voltage: V_rms = V_peak/√2, and P = V_rms^2/R. Inductance and capacitance describe reactive energy storage, not the steady heating effect. So the term describing the heating-equivalent value is the effective (RMS) value.