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RLC Series Resonance Circuit:

RLC Series Resonance Circuit Presented by: Aroosa Aslam 0513-BM


Contents Second order circuit Resistive circuit Capacitive circuit Reactance Impedance Inductive circuit RLC circuit Characteristics KVL


Contents Resonance Generic form of damping Relation of quantities Q-factor

What is second-order circuit? :

What is second-order circuit? A second-order circuit is characterized by a second-order differential equation. It consists of resistors and the equivalent of two energy storage elements. C R L U S + _ C U S + _ L R (a) series RLC circuit (b) parallel RLC circuit Typical examples of second-order circuits:

Resistive Circuit:

Resistive Circuit


Characteristics   P = VI  

Capacitive Circuit:

Capacitive Circuit




Reactance T he non-resistive component of impedance in an AC circuit, arising from the effect of inductance or capacitance or both and causing the current to be out of phase with the electromotive force causing it. It is observed for AC , but not for DC. When AC passes through a component that contains reactance, energy might be stored and released in the form of a magnetic field.


Impedance “In an AC series circuit arising from the effect of capacitance and inductance or both causing opposition to the flow of the current through electrical components as it’s the ratio of rms value of voltage and rms value of current. ”

Inductive Circuit:

Inductive Circuit



Definition of RLC Circuit:

Definition of RLC Circuit An  RLC circuit is an  electrical circuit  consisting of a resistor ( R ), an inductor ( L ), and a  capacitor ( C ), connected: in series in parallel The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC .

Series RLC Circuit:

Series RLC Circuit The series RLC circuit a bove has a single loop with the instantaneous current flowing through the loop being the same f or each circuit element .

Resistive, Capacitive and Inductive Circuit:

Resistive, Capacitive and Inductive Circuit





Vector diagram of RLC circuit:

Vector diagram of RLC circuit

Kirchhoff ’s Voltage Law:

Kirchhoff ’s Voltage Law

Formation of differential equation:

  Formation of differential equation


Resonance The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase. Thereby resulting in a purely resistive impedance. Any passive electric circuit will resonate if it has an inductor and capacitor. Resonance is characterized by the input voltage and current being in phase. The driving point impedance (or admittance) is completely real when this condition exists.

Generic waveforms corresponding to the four cases of damping.:

Generic waveforms corresponding to the four cases of damping.

Relation between Charge & Time :

Relation between Charge & Time

Relation between Voltage & Time with damping:

Relation between Voltage & Time with damping

Relation between Current & Time and Voltage Time:

Relation between Current & Time and Voltage Time

Relation between Impedance & Frequency:

Relation between Impedance & Frequency

Relation between Current & Frequency:

Relation between Current & Frequency


Q-Factor The quality factor or the Q factor of an inductor at the operating frequency ω is defined as the ratio of reactance of the coil to its resistance . The lower the value of this resistance R , the better the quality of the coil.

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