This document discusses parallel resonance in RLC circuits. It states that at resonance, voltage and current must be in phase. The resonant frequency depends on the circuit configuration and the net admittance of the circuit must be resistive. It provides examples of calculating resonant frequency and current for different RLC circuits operating at resonance.

1. RESONANCE

2. ELE101/102 Dept of E&E,MIT Manipal 2
PARALLEL RESONANCE - Characteristics
At Resonance Voltage and current must be in phase.
The resonant frequency depends on circuit
configuration
Net admittance of the circuit must be resistive in
nature
Hence, find the net admittance of the circuit and
equate the imaginary part to zero.
The admittance of the circuit is minimum at resonance
Power factor is unity
Net susceptance is zero

3. ELE101/102 Dept of E&E,MIT Manipal 3
PARALLEL RESONANCE
R
L
C
v(t)v(t)
R L
iR iCiL
C
R L
L
C
v(t)
R C

4. ELE101/102 Dept of E&E,MIT Manipal 4
Resonant frequency (fr)
Example: For the Circuit shown…
ωCj
ωC
1
j
1
Z
1
Yˆ;
ωC
1
jjXZˆ
ωL)((R)
ωL)(R
YˆωL);(R)jX(RZˆ
2
2C2
221L1
=






−
==−=−=
+
+
=+=+= R
L
C
v(t)
Cj
)L(R
L
j
)L(R
R
YYY 2222
21 ω+
ω+
ω
−
ω+
=+=
2
r
2
)L(R
L
C
ω+
=
2
r
L
R
LC
1
2
1
f 





−
π
=
2
1






−=
L
R
LC
rω
Note: The expression for resonant frequency depends on circuit
configuration.

5. ELE101/102 Dept of E&E,MIT Manipal 5
Variation of current:
I
ωωro
At resonance Current is minimum
Rejector circuit

6. ELE101/102 Dept of E&E,MIT Manipal 6
Tutorial
[1] A series RLC circuit consisting of R=100Ω, L=10mH and
C=100μF is supplied by an ac supply of 100 volt at varying
frequency. Determine
a) Current at resonance
b) Resonant frequency
c) Half power frequencies
d) Q factor
rad/sec10099ωrad/sec,99ω
0.1,Q159.15Hz,f1A,I
:Ans
21
00
==
===

7. ELE101/102 Dept of E&E,MIT Manipal 7
Tutorial
[2] An RLC series circuit of R=8Ω resistance should be designed to
have a bandwidth of 50 Hz. Determine the value of L and C so that
the system resonates at 200 Hz
F24.86C
46.25
:
µ=
= mHL
Ans

8. ELE101/102 Dept of E&E,MIT Manipal 8
Tutorial
[3] The parallel circuit shown in figure is made to resonate by varying L.
Find the value of L if ω=5000rad/sec
2 Ω 5 Ω
L 2 0 µ F
Ans:
XL = 12.17 Ω or 0.3286Ω
L = 65.73μH or 2.434mH

9. ELE101/102 Dept of E&E,MIT Manipal 9
Tutorial
v s = C o s ( 1 . 4 t )
L = 0 . 5 H C = 1 F
5 Ω
[4] Show that circuit given in figure will be at resonance at
supply frequency
rad/sec1.4atresistivepurely099.0Z =ω−−−=

10. ELE101/102 Dept of E&E,MIT Manipal 9
Tutorial
v s = C o s ( 1 . 4 t )
L = 0 . 5 H C = 1 F
5 Ω
[4] Show that circuit given in figure will be at resonance at
supply frequency
rad/sec1.4atresistivepurely099.0Z =ω−−−=