A.C. Fundamentals - Resonance in Parallel A.C. Circuits (Parallel Resonance)
1 Answer
Parallel resonance, also known as anti-resonance, is a phenomenon that occurs in parallel AC circuits when the impedance of the circuit is minimized and the current flowing through the circuit becomes maximum at a particular frequency. This happens when the inductive reactance (XL) and capacitive reactance (XC) in the circuit cancel each other out.
Key points about parallel resonance in AC circuits:
Components in a Parallel Resonant Circuit:
A parallel resonant circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel.
The resistor represents the resistance of the circuit components and any external load.
The inductor introduces inductive reactance (XL) which opposes changes in current.
The capacitor introduces capacitive reactance (XC) which opposes changes in voltage.
Resonant Frequency (f_r):
The resonant frequency is the frequency at which the impedance of the circuit is minimum.
It is given by the formula: f_r = 1 / (2Ďâ(LC)), where L is the inductance and C is the capacitance of the circuit.
Impedance at Resonance:
At resonance, the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude but opposite in phase, causing them to cancel each other out.
The impedance (Z) of the circuit becomes purely resistive, and its value is equal to the resistance (R) of the circuit: Z = R.
Current at Resonance:
Due to the purely resistive impedance at resonance, the current flowing through the circuit becomes maximum.
The current is limited only by the resistance in the circuit, and the current amplitude can become very high.
Voltage across Components:
The voltage across the inductor and capacitor is out of phase with each other, and they can be of considerable magnitudes.
The voltage across the resistor is in phase with the current.
Applications:
Parallel resonance is used in various applications, such as in tuning circuits in radio receivers and transmitters, where it is used to select a specific frequency from a range of frequencies.
Bandwidth and Quality Factor (Q):
The bandwidth of the parallel resonant circuit is the range of frequencies around the resonant frequency where the impedance remains relatively low.
The quality factor (Q) of the circuit describes the selectivity and sharpness of the resonance. It is given by the formula: Q = f_r / BW, where BW is the bandwidth.
Damping and Overdamping:
Damping refers to the dissipation of energy in the circuit due to resistive elements.
Overdamping occurs when the circuit has a higher resistance, causing the impedance curve to be wide and flat around the resonant frequency.
Understanding parallel resonance in AC circuits is important in various fields of electronics and electrical engineering, as it provides insights into circuit behavior and performance.
Key points about parallel resonance in AC circuits:
Components in a Parallel Resonant Circuit:
A parallel resonant circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel.
The resistor represents the resistance of the circuit components and any external load.
The inductor introduces inductive reactance (XL) which opposes changes in current.
The capacitor introduces capacitive reactance (XC) which opposes changes in voltage.
Resonant Frequency (f_r):
The resonant frequency is the frequency at which the impedance of the circuit is minimum.
It is given by the formula: f_r = 1 / (2Ďâ(LC)), where L is the inductance and C is the capacitance of the circuit.
Impedance at Resonance:
At resonance, the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude but opposite in phase, causing them to cancel each other out.
The impedance (Z) of the circuit becomes purely resistive, and its value is equal to the resistance (R) of the circuit: Z = R.
Current at Resonance:
Due to the purely resistive impedance at resonance, the current flowing through the circuit becomes maximum.
The current is limited only by the resistance in the circuit, and the current amplitude can become very high.
Voltage across Components:
The voltage across the inductor and capacitor is out of phase with each other, and they can be of considerable magnitudes.
The voltage across the resistor is in phase with the current.
Applications:
Parallel resonance is used in various applications, such as in tuning circuits in radio receivers and transmitters, where it is used to select a specific frequency from a range of frequencies.
Bandwidth and Quality Factor (Q):
The bandwidth of the parallel resonant circuit is the range of frequencies around the resonant frequency where the impedance remains relatively low.
The quality factor (Q) of the circuit describes the selectivity and sharpness of the resonance. It is given by the formula: Q = f_r / BW, where BW is the bandwidth.
Damping and Overdamping:
Damping refers to the dissipation of energy in the circuit due to resistive elements.
Overdamping occurs when the circuit has a higher resistance, causing the impedance curve to be wide and flat around the resonant frequency.
Understanding parallel resonance in AC circuits is important in various fields of electronics and electrical engineering, as it provides insights into circuit behavior and performance.