Average Power in an AC Circuit
The instantaneous power at any one moment is the same as in a DC circuit - Joules Law
The average power is the time average of the power over one period.
For a current driven circuit we can rewrite this as,
This equations can be applied to any of the components in an RLC circuit or the oscillator driving the circuit.
Inductor: f = p/2 and cos(p/2) = 0
Thus an ideal inductor can not dissipate any energy, it can only store energy.
Capacitor: f = -p/2 and cos(-p/2) = 0
Thus an ideal capacitor can not dissipate any energy, it can only store energy.
Resistor: f = 0 and cos(0) = 1
Thus only the resistor can dissipate energy as heat. Since Z = R for a resistor,
Oscillator: Z is the impedance of the RLC curcit elements. Since the maximum voltage generated by the oscillator is related to the maximum current by
We can rewrite the average power as,
This represents the power that the oscillator must supply to drive the circuit which is also identical to the power dissipated by the resistor. Note that the maximum/rms voltage generated by the oscillator is not equal to the maximum/rms voltage across the resistor except when the circuit is in resonance where f = 0.
Power Factor: The term cos(f) is called the power factor of RLC circuit. The power factor is often expressed as a percentage (between 0% and 100%) and is a measure of the percentage of the maximum power that the circuit could deliver if it was driven at resonance.