Parallel Resonance
In a parallel resonance circuit, the inductor (L) and capacitor (C) are connected in parallel, with a resistor (R) typically in series with the inductor. At the resonant frequency (f₀), the impedance of the inductor and capacitor cancel each other out, resulting in a sharp increase in current flow through the circuit.
The resonance occurs when the instantaneous values of currents IL and IC are equal and opposite to each other.
Applying KCL to this parallel RLC circuit we get,
I=IR+IL+IC
According to Ohm’s law,
IR=V/R; IL=V/jXL; IC=V/(-jXC)
Therefore, the total circuit current is given by,
I=V/R+V/jXL-V/(jXC)
Hence, I=VY
Where,
Y=1/R+j(1/XC-1/XL)
Condition of Parallel Resonance
XL=XC
Electrical Quantities at Parallel Resonance
- Resonance Frequency: The resonance frequency of a parallel resonance circuit is the value of the supply frequency where the inductive reactance XL becomes equal to the capacitive reactance XC i.e.
XL=XC
2πfL=1/2πfC
f2=1/4π2LC
fr=1/2π√LC
Also,
ωr=1/√LC
The resonant frequency of a parallel RLC circuit depends on the value of capacitance and inductance.
- Impedance: At resonance the value of circuits admittance is minimum which disrupts the flow of electric current.
The impedance of the circuit is maximum at resonance and the circuit draws minimum current.
Z=R
- Admittance: Admittance is the measuring ability of the current through a device or circuit. This is the inverse of impedance which is similar to how conductance is related to resistance. The SI unit of admittance is the siemens represented by symbol S.
Admittance is given by: Y=1/R+j(1/XC-1/XL)
At resonance: XL=XC
Putting it in the admittance equation we get
Y=1/R
At resonance the admittance Y being equal to the resistance reciprocal.
Voltage: Voltage refers to the potential difference across each branch of the circuit. In Parallel circuit the voltage remains the same across each branch.
At parallel resonance,
XC=XL
Therefore,
I=VR
V=IR
At parallel resonance the voltage across each element will be equal to the voltage across the resistance. This is the maximum value of the voltage that appears across each element.
- Current: Current is the flow of electric charge through each individual branch of the circuit. In parallel circuit total current splits among the various branches based on their individual resistances or impedances. The circuit current I at parallel resonant condition is given by,
I=IR
- Quality Factor: At parallel resonance,
fr=1/2π√LC
Q=R√C/L
- Bandwidth: The difference in upper frequency and lower frequency denotes the bandwidth of the parallel resonance circuit. The power dissipation at the upper and lower frequencies is half of the full power dissipated at the resonance frequency fr.
The bandwidth of the parallel resonance circuit is expressed by the following formula.
BW=fupper-flower
BW=fr/Q
What is Resonance ?
Resonance in electric circuits is a phenomenon that plays a vital role in changing the behavior of circuits and the transmission of electrical signals. Resonance plays a crucial role in various applications ranging from tuning radio frequencies to enhancing power transfer in electrical systems. This function takes place at a particular constant frequency, at the moment when impedance and reactance cancel out each other. In this article, we will go through the resonance in electric circuits and how it affects them, the types and applications which are widely used in many devices.
Table of Content
- What is Resonance?
- Key Components
- Effect of Resonance
- Characteristics
- Types
- Differentiate between series and parallel resonance
- Application
- Advantages
- Disadvantages