Which quantity is used to compute the heating effect of current in AC circuits?

Which quantity is used to compute the heating effect of current in AC circuits?

• A. RMS
• B. Peak
• C. Average
• D. Frequency

Answer: (A)

In AC circuits, the heating effect in a conductor or resistor comes from the power dissipated, which is proportional to the square of the current: P = i^2 R. To express this heating as a single current value that would produce the same heating if it were a steady DC current, we use the root-mean-square (RMS) current. The RMS value represents the effective current over time. For a sinusoidal current i(t) = I_peak sin(ωt), the instantaneous power is i^2(t)R = I_peak^2 sin^2(ωt)R. Averaging over a full cycle gives P_avg = (I_peak^2/2) R. This is exactly equal to (I_rms)^2 R, where I_rms = I_peak/√2. So the heating effect of the AC current is the same as that of a constant current equal to the RMS value. The peak current tells you the maximum current reached, but not how the heating sums up over time. The average current by itself can be zero for symmetric waves and doesn’t reflect the heating which depends on i^2. Frequency doesn’t set the heating directly; it affects reactance and impedance but not the average power dissipated in a purely resistive path.

In AC circuits, the heating effect in a conductor or resistor comes from the power dissipated, which is proportional to the square of the current: P = i^2 R. To express this heating as a single current value that would produce the same heating if it were a steady DC current, we use the root-mean-square (RMS) current. The RMS value represents the effective current over time.

For a sinusoidal current i(t) = I_peak sin(ωt), the instantaneous power is i^2(t)R = I_peak^2 sin^2(ωt)R. Averaging over a full cycle gives P_avg = (I_peak^2/2) R. This is exactly equal to (I_rms)^2 R, where I_rms = I_peak/√2. So the heating effect of the AC current is the same as that of a constant current equal to the RMS value.

The peak current tells you the maximum current reached, but not how the heating sums up over time. The average current by itself can be zero for symmetric waves and doesn’t reflect the heating which depends on i^2. Frequency doesn’t set the heating directly; it affects reactance and impedance but not the average power dissipated in a purely resistive path.