Page 18 - 12-phy-16 ALTERNATING CURRENT

16. Alternating Current eLearn.Punjab

The impedance diagram of the circuit is shown in Fig. 16.13 (b). As explained earlier, the inductive

reactance X = wL and capacitor reactance X = 1/ wC are directed opposite to each other. When
C
L
the frequency of A.C. source is very small much greater than
X = wL. So the capacitance dominates at low frequencies and
L
the circuit behaves like an R - C circuit. At high frequencies X =
L
wL is much greater than X = 1/ wC. In this case the inductance
C
dominates and the circuit behaves like R - L circuit. In between

these frequencies there will be a frequency w , at which X =
r
L
Fig. 16.13 (b) X . This condition is called resonance. Thus at resonance the
C
inductive reactance being equal and opposite to capacitor
reactance, cancel each other and the impedance diagram assumes the form (Fig. 16.13 c). The

value of the resonance frequency can be obtained by putting
1
Lw= w C
r

1 r 1
or w = LC or w= LC
2
r
r
Fig. 16.13 (c) 1
or f = ....... (16.18)
r
2p LC

The following are the properties of the series resonance circuit.
i) The resonance frequency is given by
1
f =
r
2p LC

ii) The impedance of the circuit at resonance
is only resistive so the current and voltage

are in phase. The power factor is 1.
iii) The impedance of the circuit is minimum

at this frequency and it is equal to R.
iv) If the amplitude of the source voltage V
o
is constant, the current is maximum at
the resonance frequency and its value is

V / R. The variation of current with the
o
frequency is shown in Fig. 16.14.
v) At resonance V , the voltage drop across
L
inductance and V the voltage drop across
C
capacitance may be much larger than the Fig. 16.14

source voltage.
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