Resonance in series and parallel circuits

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1. MECHANICAL DEPARTMENT Elements of Electrical Engineering ACTIVE LEARNING ASSIGNMENT Topic: Resonance in series and parallel circuits Guided by: Prof. Rahish Gandhinagar Institute of Technology

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.

5. Series Resonance Circuit

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 Total impedance of series RLC Circuit is At resonance The impedance now reduce to 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

9. Half-power Frequency 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. Bandwidth,  Bandwidth,  is define as the difference between the two half power frequencies. The width of the response curve is determine by the bandwidth.

11. Current Response Curve

12. Voltage Response Curve

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.

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. Parallel Resonance

16. Parallel Resonance The total admittance Resonance occur when

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. Parameters in Parallel Circuit Parallel resonant circuit has same parameters as the series resonant circuit. Resonance frequency Half-power frequencies

19. Parameters in Parallel Circuit Bandwidth Quality Factor

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