7.3 : 周期波形的有效值

Consider an AC circuit with a periodic voltage source connected to a resistor.

The average power delivered to the resistor equals the integral of the instantaneous power over a period divided by the period.

When this resistor is connected to a DC source, the average power it absorbs is the product of the current squared and its resistance.

Considering that the average power delivered by a DC source to the resistor is equivalent to that provided by the periodic current, the direct current is equal to the effective value of the periodic current.

So, the effective value of current is the square root of the average of the squared instantaneous current values.

Similarly, the expression for the effective value of voltage can be obtained.

For any periodic signal, the effective value, also known as the root-mean-square value, is equal to the square root of the mean of the square of the periodic signal.

For a sinusoidal current and voltage, the RMS value equals the peak value divided by the square root of two.