Page 74 - Circuit Analysis II with MATLAB Applications

Chapter 2 Resonance

Parallel Resonance Curves
|Y| ZC

Magnitude of Admittance 0 G Z 0 1 / ZL Z

ZC 1/ZL

Radian Frequency

Figure 2.9. The components of Y in a parallel RLC circuit

We observe that at this parallel resonant frequency,

Y = G (2.16)
0
and
T = 0 (2.17)
Y
Example 2.2

,
t
t
t
For the circuit of Figure 2.10, i t = 10cos 5000t mA . Compute i i , and i .
L
G
C
S
+
G L i C i
t
t
t
vt i ` L C
G
– 1 4 PF
i t 0.01: 10 mH
S
Figure 2.10. Circuit for Example 2.2
Solution:
The capacitive and inductive susceptances are
B = ZC = 5000 u 4 u 10 – 6 = 0.02 : – 1
C
and
1
1
B = ------- = ----------------------------------------- = 0.02 : – 1
L
ZL 5000 u 10 u 10 – 3
and sinceB = B C , the given circuit operates at parallel resonance with Z = 5000 rad s . Then,
e
L
0
2-8 Circuit Analysis II with MATLAB Applications
Orchard Publications