Page 68 - Circuit Analysis II with MATLAB Applications

Chapter 2 Resonance

Series Resonance Curves
|Z| ZL

Magnitude of Impedance 0 R Z 0 1 / ZC Z

ZL 1 / ZC
Radian Frequency

Figure 2.2. The components of Z in a series RLC circuit

The frequency at which the capacitive reactance X C = 1 ZC and the inductive reactance X = ZL
e
L
f
are equal is called the resonant frequency. The resonant frequency is denoted as Z 0 or and these
0
can be expressed in terms of the inductance and capacitance by equating the reactances, that is,
C
L
1
Z L = ----------
0
Z C
0
1
2
Z = -------
0
LC
1
Z = ----------- (2.5)
0
LC
and
1
f = ------------------ (2.6)
0
2S LC
We observe that at resonance Z = R where Z 0 denotes the impedance value at resonance, and
0
T = 0 . In our subsequent discussion the subscript zero will be used to indicate that the circuit vari-
Z
ables are at resonance.

Example 2.1

For the circuit shown in Figure 2.3, compute I 0 , Z 0 , , V R0 , V L0 , and V C0 . Then, draw a phasor
C
diagram showing V R0 , V L0 , and V C0 .

2-2 Circuit Analysis II with MATLAB Applications

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