Equations & Formulas For RLC Circuits (Series & Parallel)
RLC Circuits – Series & Parallel Equations & Formulas
RLC Circuit:
When a resistor, inductor and capacitor are connected together in parallel or series combination, it operates as an oscillator circuit (known as RLC Circuits) whose equations are given below in different scenarios as follow:
Parallel RLC Circuit
When they are connected in parallel combination
Impedance:
Total impedance of the circuit is;
Where
- XL = Inductive reactance
- XC = Capacitive reactance
Power Factor:
The power factor for this circuit is
Cos θ = Z/R
Resonance Frequency:
When inductive reactance XL & capacitive reactance Xc of the circuit is equal.
Where
- L = Inductance of inductor
- C = Capacitance of capacitor
Quality Factor:
It is the ratio of stored energy to the energy dissipated in the circuit.
Bandwidth:
B.W = fr / Q
Resonant Circuit Current:
The total current through the circuit when the circuit is at resonance.
At resonance, the XL = XC , so Z = R
IT = V/R
Current Magnification
Parallel resonance RLC circuit is also known current magnification circuit. Because, current flowing through the circuit is Q times the input current
Imag = Q IT
Characteristic Equation:
Neper Frequency For Parallel RLC Circuit:
Resonant Radian Frequency For Parallal RLC Circuit:
Voltage Response:
- Over-Damped Response
When
ω02 < α2
The roots s1 & s2 are real & distinct
- Under-Damped Response
When
ω02 > α2
The roots s1 & s2 are complex & conjugate of each other
- Critically Damped Response
When
ω02 = α2
The roots s1 & s2 are real & equal.
- Related Posts: Analysis of a Simple R-L Circuit with AC and DC Supply
Series RLC Circuit:
Impedance:
The total impedance of the series RLC circuit is;
Power Factor:
The power factor of Series RLC circuit;
Cos θ = R/Z
Resonance Frequency:
The frequency at which the inductive reactance XL = Capacitive reactance Xc is known as resonance frequency.
Where
- L = Inductance of the inductor
- C = Capacitance of the capacitor
Quality Factor:
Bandwidth:
B.W = (fr / Q)
- B.W = (R / L) in rad/s
- B.W = (R / 2πL) in hz
Lower Cutoff Frequency & Upper Cutoff Frequency:
fh = fr + ½ B.W
fl = fr – ½ B.W
Characteristic Equation:
Neper Frequency For series RLC Circuit:
Resonant Radian Frequency For series RLC Circuit:
Voltage Response:
- Over-Damped Response
When
ω02 < α2
The roots s1 & s2 are real & distinct
- Under-Damped Response
When
ω02 > α2
The roots s1 & s2 are complex & conjugate of each other
- Critically Damped Response
When
ω02 = α2
The roots s1 and s2 are real & equal
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