Conservation of energy requires that, at any particular time, the rate at which energy is supplied by the source of EMF must equal the rate at which it is stored in the capacitive and inductive elements; plus the rate at which it is dissipated in the resistive element (we assume ideal capacitive and inductive elements have no internal resistances).
Let E = Eosin wt. Since current lags in inductive dominated circuit by an angle q.If dw be the work done by a source of EMF e on a charge dq, then
The power

Using equations (1) and (2),








The quantity cosq is called the power factor of the AC circuit and we know
Recall the diagram to determine effective voltage in LCR circuit.
This can also be represented in terms of the resistance and reactances as follows (Since I is same through all resistive element).
Such a right-angled triangle whose sides represent the resistance and reactance an AC circuit is called the impedance triangle.
From this triangle:
Special cases
Case 1:
For a pure resistance in AC circuit
q = O therefore inr = Erms Irms
The shaded portion in the graph indicates that power delivered to the a.c circuit by the source of e.m.f is maximum and the circuit is purely resistive.
Case 2:
For a pure inductor in AC circuit, cosq = 90o P = O. i.e., Average power over a complete cycle of AC through an ideal inductor is zero. i.e., whatever energy is needed in building up current in L is returned back during the decay of the current.
The shaded portion of the graph indicates that on adding portion I, II, III and IV, vector p is equal to zero.
Case 3:
When a pure capacitance is contacted in AC circuit f= 90o or r = 0. i.e., Average power supplied to an ideal capacitor by the source over a complete cycle of A.C. is also zero.
Power Factor
P = Erms Irms cosq. The product Erms Irms is called apparent power, whereas the P is called the true power. The term cosf is called the power factor.The current through pure L or pure C, which consumes no power for its maintenance in the circuit is called wattless or idle current.
Resonance Curve
The graph shows the variation in the peak circuit Io with the applied frequency of the a.c source in different circuits (L and C for both are same).
Q Factor of a Series Resonant Circuit
Q stands for quality. The voltage magnification produced by series resonance is termed as Q-factor of the series resonance circuit.(i) Increasing the inductance of the coil ohmic
(ii) By decreasing the resistance of the coilHence the Q factor depends entirely upon the design of the coil.
Wattless Current
Choke Coil
The Average power consumed over a complete cycle in a practical choke coil is
P = Erms Irms cosfThe advantages of using a choke coil is not only to reduce the voltage, but also to prevent loss of electrical energy in the form of heat.








