Resonance in series and parallel circuits
-
Upload
hardikpanchal424 -
Category
Technology
-
view
353 -
download
4
description
Transcript of Resonance in series and parallel circuits
![Page 1: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/1.jpg)
MECHANICAL DEPARTMENT
Elements of Electrical Engineering
ACTIVE LEARNING ASSIGNMENT
Topic: Resonance in series and parallel circuits
Guided by: Prof. Rahish
Gandhinagar Institute of Technology
![Page 2: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/2.jpg)
Group MembersHardik Panchal (130120119115)Vivek Panchal (130120119122)Parth Panchal (130120119120)
![Page 3: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/3.jpg)
ContentSeries ResonanceParallel ResonanceImportant Parameters
Resonance Frequency, o
Half-power frequencies, 1 and 2
Bandwidth, Quality Factor, Q
Application
![Page 4: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/4.jpg)
IntroductionResonance 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.
![Page 5: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/5.jpg)
Series Resonance Circuit
![Page 6: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/6.jpg)
At ResonanceAt 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.
![Page 7: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/7.jpg)
Series Resonance
CLTotal jX-jXRZ
R
V
Z
VI m
Total
sm
Total impedance of series RLC Circuit is
At resonance
The impedance now reduce to
CL XX
R ZTotal
)X-j(XRZ CLTotal
The current at resonance
![Page 8: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/8.jpg)
Resonance FrequencyResonance frequency is the frequency where the condition of resonance occur.
Also known as center frequency.
Resonance frequency
rad/sLC
1ωo
HzLC2
1
of
![Page 9: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/9.jpg)
Half-power Frequency
rad/sLC
1
2L
R
2L
Rω
2
2
rad/s
LC
1
2L
R
2L
Rω
2
1
Half-power frequencies is the frequency when the magnitude of the output voltage or current is decrease by the factor of 1 / 2 from its maximum value.
Also known as cutoff frequencies.
![Page 10: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/10.jpg)
Bandwidth,
rad/s)( 12 cc ωωβ
rad/sL
Rβ
Bandwidth, is define as the difference between the two half power frequencies.The width of the response curve is determine by the bandwidth.
![Page 11: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/11.jpg)
Current Response Curve
![Page 12: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/12.jpg)
Voltage Response Curve
![Page 13: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/13.jpg)
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
LQ oo
![Page 14: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/14.jpg)
Q-Factor Vs BandwidthHigher value of Q,
smaller the bandwidth. (Higher the selectivity)
Lower value of Q larger the bandwidth. (Lower the selectivity)
![Page 15: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/15.jpg)
Parallel Resonance
![Page 16: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/16.jpg)
Parallel ResonanceThe total admittance
ωLωC
1
Resonance occur when
)ωω L1/Cj(R
1YTotal
321Total YYYY
C)(-j/
1
L)(j
1
R
1YTotal
CjωL
j-
R
1YTotal ω
![Page 17: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/17.jpg)
At ResonanceAt 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.
![Page 18: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/18.jpg)
Parameters in Parallel Circuit
rad/sLC
1
2RC
1
2RC
1ω
2
1
Parallel resonant circuit has same parameters as the series resonant circuit.
rad/sLC
1ωo
rad/sLC
1
2RC
1
2RC
1ω
2
2
Resonance frequency
Half-power frequencies
![Page 19: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/19.jpg)
Parameters in Parallel Circuit
RCβ
ωQ o
o
RC
112 ωωβ
Bandwidth
Quality Factor
![Page 20: Resonance in series and parallel circuits](https://reader036.fdocuments.us/reader036/viewer/2022081413/5461e7c8b1af9fba388b4bb8/html5/thumbnails/20.jpg)
THANK YOU