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Resonance in series and parallel circuits
1. MECHANICAL DEPARTMENT
Elements of Electrical Engineering
ACTIVE LEARNING ASSIGNMENT
Topic: Resonance in series and parallel circuits
Guided by: Prof. Rahish
2. Group Members
Hardik Panchal (130120119115)
Vivek Panchal (130120119122)
Parth Panchal (130120119120)
3. Content
Series Resonance
Parallel Resonance
Important Parameters
Resonance Frequency, o
Half-power frequencies, 1 and 2
Bandwidth,
Quality Factor, Q
Application
4. Introduction
Resonance is a condition in an RLC circuit in which
the capacitive and reactive reactance are equal in
magnitude, thereby resulting in a purely resistive
impedance.
Resonance circuits are useful for constructing
filters and used in many application.
6. At Resonance
At resonance, the impedance consists only resistive
component R.
The value of current will be maximum since the total
impedance is minimum.
The voltage and current are in phase.
Maximum power occurs at resonance since the power
factor is unity.
7. Series Resonance
CLTotal jX-jXRZ
R
V
Z
V
I m
Total
s
m
Total impedance of series RLC Circuit is
At resonance
The impedance now reduce to
CL XX
RZTotal
)X-j(XRZ CLTotal
The current at resonance
8. Resonance Frequency
Resonance frequency is the frequency where the
condition of resonance occur.
Also known as center frequency.
Resonance frequency
rad/s
LC
1
ωo
Hz
LC2
1
of
10. Bandwidth,
rad/s)( 12 cc ωωβ
rad/s
L
R
β
Bandwidth, is define as the difference between the
two half power frequencies.
The width of the response curve is determine by the
bandwidth.
13. Quality Factor (Q-Factor)
The ratio of resonance frequency to the bandwidth
The “sharpness” of response curve could be measured
by the quality factor, Q.
R
L
Q oo
14. Q-Factor Vs Bandwidth
Higher value of
Q, smaller the
bandwidth. (Higher
the selectivity)
Lower value of Q larger
the bandwidth. (Lower
the selectivity)
16. Parallel Resonance
The total admittance
ωL
ωC
1
Resonance occur when
)ωω L1/Cj(
R
1
YTotal
321Total YYYY
C)(-j/
1
L)(j
1
R
1
YTotal
Cj
ωL
j-
R
1
YTotal ω
17. At Resonance
At resonance, the impedance consists only
conductance G.
The value of current will be minimum since the
total admittance is minimum.
The voltage and current are in phase.