Effective Current

A nonsinusoidal current is expressed by Eq. 5-32 as follows

[5-42]

It should be remembered that the coefficients I₁, I₂, and I_k are the amplitudes of the various harmonic components in the current. If the current represented by Eq. 5-42 were passed through a noninductive resistance of R ohms, the voltage across that resistor would become

[5-43]

The average power, as read by an indicating wattmeter, consumed by the noninductive resistance R, can be expressed either as

[5-44]

or as

[5-45]

where I in Eq. 5-45 is the effective value of the current expressed by Eq. 5-42. Hence

[5-46]

which, from Eq. 5-38, becomes

or

[5-47]