Complete Guide to Series Resonance and Parallel Resonance with Derivations & Numericals
Learn series and parallel resonance with derivations, formulas, phasor diagrams, numericals, quality factor, bandwidth and real-world applications.
Series Resonance and Parallel Resonance – Complete Detailed Guide
Table of Contents
2. Basics of AC Circuits
3. RLC Circuit Overview
4. Series Resonance
5. Condition for Series Resonance
6. Resonant Frequency Formula
7. Characteristics of Series Resonance
8. Phasor Diagram in Series Resonance
9. Quality Factor in Series Resonance
10. Bandwidth in Series Resonance
11. Parallel Resonance
12. Condition for Parallel Resonance
13. Resonant Frequency in Parallel Circuit
14. Characteristics of Parallel Resonance
15. Phasor Diagram in Parallel Resonance
16. Series vs Parallel Resonance
17. Applications of Resonance
18. Practical Examples 19. Conclusion
1. Introduction to Resonance
Resonance is one of the most important phenomena in electrical engineering and physics. It occurs when a system oscillates at maximum amplitude at a specific frequency known as resonant frequency. In electrical circuits, resonance mainly occurs in RLC circuits that contain resistance, inductance, and capacitance.
When inductive reactance and capacitive reactance become equal, resonance occurs. At this condition, special electrical behaviors are observed depending on whether the components are connected in series or in parallel.
Resonance plays a crucial role in communication systems, radio transmitters, filters, oscillators, and tuning circuits.
2. Basics of AC Circuits
Alternating current circuits contain voltage and current that vary sinusoidally with time. Unlike DC circuits, AC circuits include reactance in addition to resistance.
Inductive reactance is given by XL = 2πfL. Capacitive reactance is given by XC = 1 / (2πfC). Both depend on frequency.
In AC circuits, impedance combines resistance and reactance. It determines the total opposition to current flow.
3. RLC Circuit Overview
An RLC circuit consists of resistor, inductor, and capacitor connected either in series or in parallel. These circuits are fundamental in studying resonance.
Depending on configuration, the behavior of current, voltage, and impedance changes at resonance.
4. Series Resonance
In series resonance, resistor, inductor, and capacitor are connected in series. The same current flows through all components.
At resonance, inductive reactance equals capacitive reactance. The reactive components cancel each other.
5. Condition for Series Resonance
Series resonance occurs when XL = XC.
2πfL = 1 / (2πfC)
Under this condition, impedance becomes purely resistive and minimum.
6. Resonant Frequency Formula
Resonant frequency is given by:
f₀ = 1 / (2π√LC)
This formula applies to both series and parallel resonance (ideal condition).
7. Characteristics of Series Resonance
At resonance, impedance is minimum and equal to resistance. Current becomes maximum. Power factor becomes unity. Voltage across L and C may become very large.
Series resonant circuit is also called acceptor circuit because it accepts maximum current at resonant frequency.
8. Phasor Diagram in Series Resonance
In series resonance, voltage across resistor is in phase with current. Voltage across inductor leads current by 90 degrees. Voltage across capacitor lags current by 90 degrees.
At resonance, VL and VC cancel each other.
9. Quality Factor in Series Resonance
Quality factor indicates sharpness of resonance. It is defined as:
Q = (Resonant Frequency) / (Bandwidth)
Higher Q means sharper resonance.
10. Bandwidth in Series Resonance
Bandwidth is difference between upper and lower half-power frequencies.
BW = f2 - f1
Narrow bandwidth indicates high selectivity.
11. Parallel Resonance
In parallel resonance, R, L, and C are connected in parallel. Voltage across each component is same.
At resonance, current in inductive branch equals current in capacitive branch.
12. Condition for Parallel Resonance
Parallel resonance occurs when XL = XC. Net reactive current becomes zero.
Circuit impedance becomes maximum.
13. Resonant Frequency in Parallel Circuit
Resonant frequency formula:
f₀ = 1 / (2π√LC)
Impedance becomes very high at this frequency.
14. Characteristics of Parallel Resonance
At resonance, impedance is maximum. Line current becomes minimum. Circuit acts as rejector circuit.
15. Phasor Diagram in Parallel Resonance
In parallel resonance, branch currents are 180 degrees out of phase. Supply current becomes minimum.
16. Series vs Parallel Resonance
In series resonance, impedance is minimum and current is maximum. In parallel resonance, impedance is maximum and current is minimum.
Series circuit acts as acceptor circuit. Parallel circuit acts as rejector circuit.
17. Applications of Resonance
Resonance is used in radio tuning circuits, oscillators, filters, television receivers, communication systems, and impedance matching.
It helps in frequency selection and signal amplification.
18. Practical Examples
Radio tuning uses series resonance. Parallel resonance is used in tank circuits. Filters use resonance to allow or block specific frequencies.
Wireless communication systems depend heavily on resonance principles.
19. Conclusion
Series resonance and parallel resonance are fundamental topics in electrical engineering. Understanding their behavior helps in designing filters, oscillators, and communication devices.
At resonance, special electrical characteristics appear that are useful in practical applications. Mastery of resonance concepts is essential for engineering students and professionals.
COMPARISON OF SERIES AND PARALLEL RESONANT CIRCUITS
(PRACTICAL PARALLEL RESONANT CIRCUIT IS CONSIDERED)
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