Page 385 - Basic Electrical Engineering

As the frequency is changing, both X and X will change. Inductive
L
C
reactance X will increase as the frequency, f is increasing while the
L
capacitive reactance, X will decrease with increasing frequency. The value
C
of R is independent of frequency. The variation of R, X , and X with
C
L
variation of frequency, f has been shown in Fig. 3.66 (b). It may be noted that
inductive reactance is jX and capacitive reactance is – jX , i.e., vectorially
c
L
they should be shown in opposite directions. However, in Fig. 3.66 (b) we
have shown their magnitudes only. At a frequency f , it is seen that the
0
magnitude of X is equal to X as the two curves cut at point P. Since X and
C
L
L
X are vectorially jX and – jX , the two reactances will cancel each other
L
c
C
when frequency is f . At f the impedance of the series R–L–C circuit is
0
0
equal to R which is the minimum value of Z. In Fig. 3.66 (c), X is
L
represented as jX and X is represented as −jX . The graph of X = X − X C
L
C
L
C
has also been drawn. The total impedance graph of Z shows that at f = f , Z =
0
R, i.e., at f the circuit offers minimum impedance, and hence maximum
0
current will flow through the circuit.
At minimum value of Z, the current in the circuit will be maximum as I =
V/R. This condition of the circuit when X equals X , Z = R, current is
C
L
maximum and is called the resonant condition and the frequency, f at which
0
resonance occurs is called the resonant frequency. At resonance, since X L

equals X , we can write
C