Series Resonance
In a series resonance circuit, the inductor (L) and capacitor (C) are connected in series, along with a resistor (R). The resonant frequency (f₀) is the frequency at which the inductive and capacitive reactance cancel each other out, resulting in a minimum impedance. During this point the circuit becomes highly responsive to the applied frequency.
Series Resonance Circuit
In this circuit, the voltage across the inductor and capacitor is equal, i.e.
VL=VC
At resonance frequency,
XL=XC
Where XL is the inductive reactance and XC is the capacitive reactance. Voltage can be obtain by applying KVL to the series RLC circuit.
V=VR+VL+VC
If I is the current flowing through the circuit, then
VR=IR
VL=IXL
VC=IXC
Therefore, the voltage equation can be written as
V=IR+IXL+IXC
Also, the reactance XL and Xc are given by,
XL=jωL=j2πfL
XC=1/jωC=1/j2πfL
Therefore,
V=I[R+j(ωL-1/ωC]
Hence, the above equation is in the form of V = IZ, where Z is called the impedance of the circuit i.e.
Z=R+j(ωL-1/ωC)
Electrical Quantities and Parameters at Series Resonance
- Resonance Frequency: The supply frequency at which the inductive reactance and capacitive reactance become equal to each other is called the resonance frequency. Resonant frequency is expressed when a circuit exhibits a maximum oscillatory response at a specific frequency. This is observed for a circuit that consists of an inductor and capacitor. It is denoted by fr.
At series resonance,
XL=XC
ωL=1/ωC
Here, ω = ωr, angular resonance frequency.
ωr=1/√LC
The linear resonance frequency will be,
fr=1/2π√(LC)
- Impedance: Impedance is the total opposition that the circuit presents to the flow of alternating current. It is a combination of resistance and reactance due to the presence of resistive, capacitive, and inductive elements within the circuit. The impedance of a series RLC circuit is given by,
Z=R+j(XL-Xc)
At series resonance,
XL=XC
Therefore,
Z=R
- Current: Current is the flow of electric charge through the circuit elements in a single path. In a series circuit all components like resistors, capacitors, and inductors are connected end-to-end so the same current flows through each component. At series resonance: XL = XC
Then,
I=V/R
The circuit draws current from the source only due to the resistance of the circuit which is the maximum value of the current that can flow through the series RLC circuit. The figure shows the relation between the series resonance circuit’s current, impedance, and resonance frequency.
Series Resonance
- Quality Factor: The quality factor of a series RLC circuit is defined as a ratio of energy stored in each cycle to the energy dissipated in each cycle, i.e.
Q=1/R*√L/C
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