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# Resonance in series and parallel circuits

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### Resonance in series and parallel circuits

1. 1. MECHANICAL DEPARTMENT Elements of Electrical Engineering ACTIVE LEARNING ASSIGNMENT Topic: Resonance in series and parallel circuits Guided by: Prof. Rahish
2. 2. Group Members  Hardik Panchal (130120119115)  Vivek Panchal (130120119122)  Parth Panchal (130120119120)
3. 3. Content  Series Resonance  Parallel Resonance  Important Parameters  Resonance Frequency, o  Half-power frequencies, 1 and 2  Bandwidth,   Quality Factor, Q  Application
4. 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.
5. 5. Series Resonance Circuit
6. 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. 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. 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
9. 9. Half-power Frequency rad/s LC 1 2L R 2L R ω 2 2             rad/s LC 1 2L R 2L R ω 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.
10. 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.
11. 11. Current Response Curve
12. 12. Voltage Response Curve
13. 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. 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)
15. 15. Parallel Resonance
16. 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. 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.
18. 18. Parameters in Parallel Circuit rad/s LC 1 2RC 1 2RC 1 ω 2 1                Parallel resonant circuit has same parameters as the series resonant circuit. rad/s LC 1 ωo  rad/s LC 1 2RC 1 2RC 1 ω 2 2              Resonance frequency Half-power frequencies
19. 19. Parameters in Parallel Circuit RC β ω Q o o  RC 1 12  ωωβ Bandwidth Quality Factor