Basic_Electrical_Engineering_4th_edition

...(1.16)

...(1.17)

A-C CIRCUITS

75

constant. At the extreme situation when the current through the inductor is maximum, the voltage across the capacitor is zero hence the total energy is

	L(J2I)2 = LF			...(1.13)
	2
where J2Iis the instantaneous maximum value ofthe current. At this since Ve is zero, there­
fore maximum energy stored is		LF. The power consumed per cycle is the energy per sec di­
			l2R
vided by f0 under resonance condition. Therefore PR = fu
		2n Ll2 f0	ffi0L
Hence	Q =	[2 R	R	(1.14)
Q can also be looked as the ratio of
		Time rate of change of energy stored
	Time rate ofchange of energy dissipated
	=	Reactive power absorbed by the inductor		...(1.15)
		Active power consumed by the resistor

The great advantage of this definition of Q is that it is also applicable to more complicated lumped circuits, to distributed circuits such as transmission lines and to non-electrical circuits.

Q is also a measure of the frequency selectivity ofthe circuit. A circuit with high Q will have a very sharp current response curve as compared to one which has a low value of Q. To understand this let us consider Fig. 1.19. Here we find that the current response is maximum

at f0 and on either side of f0, the current decreases sharply.

I

Fig. 1 . 1 9 Frequency selectivity.

In order to obtain quantitative analysis of this reduction in current, we specify two frequencies f1 and f at which the magnitude (XL - Xe) is equal to R.

Since at f1 the2 circuit is capacitive Xe is greater than Xv therefore, at fl' Xe - XL = R

and at f2