# Parallel RLC Circuit

Consider a RLC circuit in which resistor, inductor and capacitor are connected in parallel to each other.

This parallel combination is supplied by voltage supply, V

I

I

I

IL is the current flowing through the inductor.

θ is the phase angle difference between supply voltage and current.

For drawing the phasor diagram of parallel RLC circuit, voltage is taken as reference because voltage across each element remains the same and all the other currents i.e I

This parallel combination is supplied by voltage supply, V

_{S}. This**parallel RLC circuit**is exactly opposite to series RLC circuit. In series RLC circuit, the current flowing through all the three components i.e the resistor, inductor and capacitor remains the same, but in parallel circuit, the voltage across each element remains the same and the current gets divided in each component depending upon the impedance of each component. That is why**parallel RLC circuit**is said to have dual relationship with series RLC circuit. The total current, I_{S}drawn from the supply is equal to the vector sum of the resistive, inductive and capacitive current, not the mathematic sum of the three individual branch currents, as the current flowing in resistor, inductor and capacitor are not in same phase with each other; so they cannot be added arithmetically.Apply Kirchhoff's current law, which states that the sum of currents entering a junction or node, is equal to the sum of current leaving that node we get,

## Phasor Diagram of Parallel RLC Circuit

Let V is the supply voltage.I

_{S}is the total source current.I

_{R}is the current flowing through the resistor.I

_{C}is the current flowing through the capacitor.IL is the current flowing through the inductor.

θ is the phase angle difference between supply voltage and current.

For drawing the phasor diagram of parallel RLC circuit, voltage is taken as reference because voltage across each element remains the same and all the other currents i.e I

_{R}, I_{C}, I_{L}are drawn relative to this voltage vector. We know that in case of resistor, voltage and current are in same phase; so draw current vector I_{R}in same phase and direction to voltage. In case of capacitor, current leads the voltage by 90^{o}so, draw I_{C}vector leading voltage vector, V by 90^{o}. For inductor, current vector I_{L}lags voltage by 90^{o}so draw I_{L}lagging voltage vector, V by 90^{o}. Now draw the resultant of I_{R}, I_{C}, I_{L}i.e current I_{S}at a phase angle difference of θ with respect to voltage vector, V. Simplifying the phasor diagram, we get a simplified phasor diagram on right hand side. On this phasor diagram, we can easily apply Pythagoras's theorem and we get,## Impedance of Parallel RLC Circuit

From the phasor diagram of parallel RLC circuit we get, Substituting the value of I_{R}, I_{C}, I_{L}in above equation we get, On simplifying, As shown above in the equation of impedance, Z of a parallel RLC circuit each element has reciprocal of impedance (1/Z) i.e admittance, Y. For solving parallel RLC circuit it is convenient if we find admittance of each branch and the total admittance of the circuit can be found by simply adding each branch's admittance.### Admittance Triangle of Parallel RLC Circuit

In series RLC circuit, impedance is considered, but as stated in introduction on parallel RLC circuit, it is exactly opposite to that of series RLC circuit; so in Parallel RLC circuit, we will consider admittance. The impedance Z has two components; resistance, R and reactance, X. Similarly, admittance also has two components such as conductance, G (reciprocal of resistance, R) and suspceptance, B (reciprocal of reactance, X). So admittance triangle of parallel RLC circuit is completely opposite to that of series impedance triangle.## Resonance in Parallel RLC Circuit

Like series RLC circuit,**parallel RLC circuit**also resonates at particular frequency called resonance frequency i.e. there occurs a frequency at which inductive reactance becomes equal to capacitive reactance but unlike series RLC circuit, in parallel RLC circuit the impedance becomes maximum and the circuit behaves like purely resistive circuit leading to unity electrical power factor of the circuit.Closely Related Articles Parity GeneratorDual NetworkTime ConstantElectric Circuit or Electrical NetworkSeries Parallel Battery CellsRL Series CircuitWhat is Inductor and Inductance | Theory of InductorRLC 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 CircuitResonance in Series RLC CircuitPlanar and Non Planar Graphs of CircuitClipping CircuitMore Related Articles Series and Parallel Inductors Measurement of Insulation ResistanceElectric PowerPhase Synchronizing Device or Controlled Switching DeviceElectric Current and Theory of Electricity | Heating and Magnetic EffectNature of ElectricityDrift Velocity Drift Current and Electron MobilityRMS 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 TemperatureCircuit Elements - Active Passive Elements of Electrical CircuitElectrical DC Series and Parallel CircuitMagnetic FieldMagnetic FluxMagnetic PermeabilityHysteresis LoopMagnetic CircuitMagnetic SaturationEnergy Stored in a Magnetic FieldStatic Electric Field | Electrostatic Induction A Current Carrying Conductor within a Magnetic FieldMagnetic SusceptibilityHard Magnetic MaterialsSoft Magnetic MaterialsMagnetic Circuit with Air GapElectric ChargeCoulomb's 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 SeriesMutual 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 LDRVoltage SourceIdeal Dependent Independent Voltage Current SourceVoltage or Electric Potential DifferenceVoltage Drop CalculationVoltage DividerVoltage MultiplierVoltage DoublerVoltage RegulatorVoltage FollowerVoltage Regulator 7805Voltage to Current ConverterNew Articles Series and Parallel Inductors Electric PowerMeasurement of Losses in Shunt ReactorThree Phase Shunt ReactorMeasurement of Insulation ResistanceAmpere's Circuital Law