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Inside Collection (Course): Fundamentals of Electrical Engineering I

Summary: Re-expression of element power using impedances.

Recalling that the instantaneous power consumed by a circuit element or an equivalent circuit that represents a collection of elements equals the voltage times the current entering the positive-voltage terminal,

When all sources produce sinusoids of frequency

From another viewpoint, the real-part of complex power represents long-term energy consumption/production. Energy is the integral of power and, as the integration interval increases, the first term appreciates while the time-varying term "sloshes." Consequently, the most convenient definition of the average power consumed/produced by any circuit is in terms of complex amplitudes.

Suppose the complex amplitudes of the voltage and current have fixed magnitudes.
What phase relationship between voltage and current maximizes the average power?
In other words, how are

For maximum power dissipation, the imaginary part of complex power should be zero.
As the complex power is given by

Because the complex amplitudes of the voltage and current are related by the equivalent impedance, average power can also be written as
*Only the real part of impedance contributes to long-term power dissipation*.
Of the circuit elements, *only* the resistor dissipates power.
Capacitors and inductors dissipate no power in the long term.
It is important to realize that these statements apply only for sinusoidal sources.
If you turn on a constant voltage source in an RC-circuit, charging the capacitor does consume power.

In an earlier problem, we found that the rms value of a sinusoid was its amplitude divided by

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