The RLC Series Circuit
The RLC Series Circuit
The denominator of the fraction plays the role of resistance and is called the impedance Z of the circuit:
The phase angle φ between the current and the voltage is 
The RLC Series Circuit
Power in an AC Circuit
The instantaneous power P as
The average power
where the quantity cosφ is called the power factor
Power in an AC Circuit
The average power delivered by the source is converted to internal energy in the resistor,
Power in an AC Circuit
No power losses are associated with pure capacitors and pure inductors in an AC circuit.
The average power supplied by the source is zero. In other words, no power losses occur in a capacitor in an AC circuit.
Resonance in a Series RLC Circuit
A series RLC circuit is said to be in resonance when the current has its maximum value.
The frequency ω0 at which XL - XC = 0 is called the resonance frequency of the circuit.
Resonance in a Series RLC Circuit
Let’s calculate the average power as a function of frequency for a series RLC circuit. 
At resonance, when ω=ω0, the average power is a maximum and has the value (ΔVrms)2/R.
Resonance in a Series RLC Circuit
(a) The rms current versus frequency for a series RLC circuit, for three values of R. The current reaches its maximum value at the resonance frequency ω0. (b) Average power
delivered to the circuit versus frequency for the series RLC circuit, for two values of R.
Resonance in a Series RLC Circuit
The quality factor, denoted by Q:
where Δω is the width of the curve measured between the two values of ω for which Pav has half its maximum
value, called the half-power points