Discharging a Capacitor
Charging a Capacitor
Parity GeneratorClosely Related Articles
Electric Circuit and Electrical Circuit Elements
Series Parallel Battery Cells
RL Series Circuit
Three Phase Circuit | Star and Delta System
RL Parallel Circuit
RL Circuit Transfer Function Time Constant RL Circuit as Filter
Construction of AC Circuits and Working of AC Circuits
Series RLC Circuit
Parallel RLC Circuit
Resistances in Series and Resistances in Parallel
Resonance in Series RLC Circuit
Planar and Non Planar Graphs of Circuit
Nature of Electricity
Current and Voltage Division Rule
Working of Capacitor
Transient Behavior of Capacitor
Capacitors in Series and Parallel
Testing of Capacitors
Electrical Conductance Conductivity of Metal Semiconductor and Insulator | Band Theory
What is Electrical Resistance?
Resistivity and Laws of Resistance
Properties of Electric Conductor
Temperature Coefficient of Resistance
Resistance Variation with Temperature
Active & Passive Elements
Maximum Power Transfer Theorem
Star - Delta Transformation
Static Electric Field | Electrostatic Induction
Magnetic Field and Magnetic Circuit | Magnetic Materials
Energy Stored in a Magnetic Field
A Current Carrying Conductor Within A Magnetic Field
Hard Magnetic Materials
Soft Magnetic Materials
Magnetic Circuit with Air Gap
Lines of Force
What is Flux
Capacitor and Capacitance
Energy Stored in Capacitor
Charging a Capacitor
Discharging a Capacitor
Fourier Series and Fourier Transform
Trigonometric Fourier Series
Analysis of Exponential Fourier Series
What is Inductor and Inductance | Theory of Inductor
SI System of Units
Electrical International Symbol
Electric Power Single and Three Phase Power Active Reactive Apparent
Vector Algebra | Vector Diagram
Relationship of Line and Phase Voltages and Currents in a Star Connected System
Vector Diagram | Three Phase Vector Diagram
Carbon Composition Resistor
Wire Wound Resistor
Light Dependent Resistor
Source of Electrical Energy
Ideal Dependent Independent Voltage Current Source
Voltage in Series
Voltage in Parallel
Voltage Drop Calculation
Voltage Regulator 7805
Voltage to Current Converter
Resonance in Series RLC Circuit
- When a current flows in an inductor, energy gets stored in magnetic field.
- When a capacitor is charged, energy gets stored in static electric field.
The magnetic field in the inductor is built by the current, which is provided by the discharging capacitor. Similarly, the capacitor is charged by the current produced by collapsing magnetic field of inductor and this process continues on and on, causing electrical energy to oscillate between the magnetic field and the electric field. In some cases, at certain frequency called resonant frequency, the inductive reactance of the circuit becomes equal to capacitive reactance which causes the electrical energy to oscillate between the electric field of the capacitor and magnetic field of the inductor. This forms a harmonic oscillator for current. In RLC circuit, the presence of resistor causes these oscillation to die out over period of time and is called damping effect of resistor.
Variation in Inductive Reactance and Capacitive Reactance with Frequency
Variation of Inductive Reactance Vs FrequencyWe know that inductive reactance XL = 2πfL means inductive reactance is directly proportional to frequency (XL and prop ƒ). When the frequency is zero or in case of DC, inductive reactance is also zero, the circuit acts as a short circuit; but when frequency increases; inductive reactance also increases. At infinite frequency, inductive reactance becomes infinity and circuit behaves as open circuit. It means that, when frequency increases inductive reactance also increases and when frequency decreases, inductive reactance also decreases. So, if we plot a graph between inductive reactance and frequency, it is a straight line linear curve passing through origin as shown in the figure above.
Variation of Capacitive Reactance Vs FrequencyIt is clear from the formula of capacitive reactance XC = 1 / 2πfC that, frequency and capacitive reactance are inversely proportional to each other. In case of DC or when frequency is zero, capacitive reactance becomes infinity and circuit behaves as open circuit and when frequency increases and becomes infinite, capacitive reactance decreases and becomes zero at infinite frequency, at that point the circuit acts as short circuit, so the capacitive reactance increases with decease in frequency and if we plot a graph between capacitive reactance and frequency, it is an hyperbolic curve as shown in figure above.
Inductive Reactance and Capacitive Reactance Vs FrequencyFrom the above discussion, it can be concluded that the inductive reactance is directly proportional to frequency and capacitive reactance is inversely proportional to frequency, i.e at low frequency XL is low and XC is high but there must be a frequency, where the value of inductive reactance becomes equal to capacitive reactance. Now if we plot a single graph of inductive reactance vs frequency and capacitive reactance vs frequency, then there must occur a point where these two graphs cut each other. At that point of intersection, the inductive and capacitive reactance becomes equal and the frequency at which these two reactances become equal, is called resonant frequency, fr. At resonant frequency, XL = XL At resonance f = fr and on solving above equation we get,
Variation of Impedance Vs FrequencyAt resonance in series RLC circuit, two reactances become equal and cancel each other. So in resonant series RLC circuit, the opposition to the flow of current is due to resistance only. At resonance, the total impedance of series RLC circuit is equal to resistance i.e Z = R, impedance has only real part but no imaginary part and this impedance at resonant frequency is called dynamic impedance and this dynamic impedance is always less than impedance of series RLC circuit. Before series resonance i.e before frequency, fr capacitive reactance dominates and after resonance, inductive reactance dominates and at resonance the circuit acts purely as resistive circuit causing a large amount of current to circulate through the circuit.
Resonant CurrentIn series RLC circuit, the total voltage is the phasor sum of voltage across resistor, inductor and capacitor. At resonance in series RLC circuit, both inductive and capacitive reactance cancel each other and we know that in series circuit, the current flowing through all the elements is same, So the voltage across inductor and capacitor is equal in magnitude and opposite in direction and thereby they cancel each other. So, in a series resonant circuit, voltage across resistor is equal to supply voltage i.e V = Vr. In series RLC circuit current, I = V / Z but at resonance current I = V / R, therefore the current at resonant frequency is maximum as at resonance in impedance of circuit is resistance only and is minimum. The above graph shows the plot between circuit current and frequency. At starting, when the frequency increases, the impedance Zc decreases and hence the circuit current increases. After some time frequency becomes equal to resonant frequency, at that point inductive reactance becomes equal to capacitive reactance and the impedance of circuit reduces and is equal to circuit resistance only. So at this point, the circuit current becomes maximum I = V / R. Now when the frequency is further increased, ZL increases and with increase in ZL, the circuit current reduces and then the current drops finally to zero as frequency becomes infinite.
Power Factor at ResonanceAt resonance, the inductive reactance is equal to capacitive reactance and hence the voltage across inductor and capacitor cancel each other. The total impedance of circuit is resistance only. So, the circuit behaves like a pure resistive circuit and we know that in pure resistive circuit, voltage and the circuit current are in same phase i.e Vr, V and I are in same phase direction. Therefore, the phase angle between voltage and current is zero and the power factor is unity.
Application of Series RLC Resonant CircuitSince resonance in series RLC circuit occurs at particular frequency, so it is used for filtering and tuning purpose as it does not allow unwanted oscillations that would otherwise cause signal distortion, noise and damage to circuit to pass through it. Summary For a series RLC circuit at certain frequency called resonant frequency, the following points must be remembered. So at resonance:
- Inductive reactance XL is equal to capacitive reactance XC.
- Total impedance of circuit becomes minimum which is equal to R i.e Z = R.
- Circuit current becomes maximum as impedance reduces, I = V / R.
- Voltage across inductor and capacitor cancels each other, so voltage across resistor Vr = V, supply voltage.
- Since net reactance is zero, circuit becomes purely resistive circuit and hence the voltage and the current are in same phase, so the phase angle between them is zero.
- Power factor is unity.
- Frequency at which resonance in series RLC circuit occurs is given by
Closely Related Articles Parity GeneratorElectric Circuit and Electrical Circuit ElementsSeries Parallel Battery CellsRL Series CircuitRLC CircuitThree Phase Circuit | Star and Delta SystemRL Parallel CircuitRL Circuit Transfer Function Time Constant RL Circuit as FilterConstruction of AC Circuits and Working of AC CircuitsSeries RLC CircuitParallel RLC CircuitResistances in Series and Resistances in ParallelPlanar and Non Planar Graphs of CircuitClipping CircuitMore Related Articles Electric Current and Theory of Electricity | Heating and Magnetic EffectNature of ElectricityDrift Velocity Drift Current and Electron MobilityElectric Current and Voltage Division RuleRMS or Root Mean Square Value of AC SignalWorking Principle of a CapacitorQuality Factor of Inductor and CapacitorTransient Behavior of CapacitorCylindrical CapacitorSpherical CapacitorCapacitors in Series and ParallelHow to Test Capacitors?Electrical Conductance Conductivity of Metal Semiconductor and Insulator | Band TheoryWhat is Electrical Resistance?Resistivity and Laws of ResistanceProperties of Electric ConductorTemperature Coefficient of ResistanceResistance Variation with TemperatureSeries ResistanceActive and Passive Elements of Electrical CircuitElectrical DC Series and Parallel CircuitOhm's Law | Equation Formula and Limitation of Ohm's LawKirchhoff Current Law and Kirchhoff Voltage LawSingle and Multi Mesh AnalysisSuperposition TheoremThevenin Theorem and Thevenin Equivalent Voltage and ResistanceNorton Theorem | Norton Equivalent Current and ResistanceReciprocity TheoremNodal Analysis in Electric CircuitsMaximum Power Transfer TheoremDelta - Star transformation | Star - Delta TransformationMagnetic FieldStatic Electric Field | Electrostatic Induction Magnetic PermeabilityMagnetic Field and Magnetic Circuit | Magnetic MaterialsMagnetic SaturationEnergy Stored in a Magnetic FieldHysteresis LoopA Current Carrying Conductor Within A Magnetic FieldMagnetic SusceptibilityHard Magnetic MaterialsSoft Magnetic MaterialsMagnetic Circuit with Air GapElectric ChargeCoulombs Law | Explanation Statement Formulas Principle Limitation of Coulomb’s LawElectric Lines of ForceWhat is Electric Field?Electric Field Strength or Electric Field IntensityWhat is Flux? Types of Flux?Electric FluxElectric PotentialCapacitor and Capacitance | Types of CapacitorsEnergy Stored in CapacitorCharging a CapacitorDischarging a CapacitorFourier Series and Fourier TransformTrigonometric Fourier SeriesAnalysis of Exponential Fourier SeriesWhat is Inductor and Inductance | Theory of InductorMutual InductanceSelf InductanceSI System of UnitsElectrical International SymbolElectric Power Single and Three Phase Power Active Reactive ApparentVector Algebra | Vector DiagramRelationship of Line and Phase Voltages and Currents in a Star Connected SystemVector Diagram | Three Phase Vector DiagramTypes of Resistor Carbon Composition and Wire Wound ResistorVaristor Metal Oxide Varistor is Nonlinear ResistorCarbon Composition ResistorWire Wound ResistorVariable Resistors | Defination, Uses and Types of Variable ResistorsLight Dependent Resistor | LDR and Working Principle of LDRSource of Electrical EnergyVoltage SourceIdeal Dependent Independent Voltage Current SourceVoltage or Electric Potential DifferenceVoltage in SeriesVoltage in ParallelVoltage Drop CalculationVoltage DividerVoltage MultiplierVoltage DoublerVoltage RegulatorVoltage FollowerVoltage Regulator 7805Voltage to Current ConverterNew Articles Ring CounterDischarging a CapacitorCharging a CapacitorElectric PotentialParity Generator