Online Electrical Engineering
Space for Adverticement

Nature of Electricity
Drift Velocity Drift Current and Electron Mobility
Electric Current and Theory of Electricity | Heating & Magnetic Effect
Voltage or Electric Potential Difference
Atomic Structure
Electrical Conductance Conductivity of Metal Semiconductor and Insulator | Band Theory
Electrical Resistance and Laws of Resistance
SI System of Units
Ideal Dependent Independent Voltage Current Source
Series Parallel Battery Cells
Single and Multi Mesh Analysis
Kirchhoff Current Law and Kirchhoff Voltage Law
Superposition Theorem
Reciprocity Theorem
Compensation Theorem
Electric Power Single and Three Phase Power Active Reactive Apparent
Types of resistor Carbon Composition and Wire Wound Resistor
Varistor Metal Oxide Varistor is nonlinear Resistor
Principle of Electrolysis of Copper Sulfate Electrolyte
Construction of Lead Acid Battery
Voltaic Cell
Norton Theorem | Norton Equivalent Current and Resistance
Maximum Power Transfer Theorem
Working of Lead Acid Battery | Lead Acid Secondary Storage Battery
Fleming Left Hand rule and Fleming Right Hand rule
Ohms Law | Equation Formula and Limitation of Ohms Law
Electrical DC Series and Parallel Circuit
Ionization Process and Definition
Faraday First and Second Laws of Electrolysis
Applications of Electrolysis Electroplating Electroforming Electrorefining
Resistances in Series and Resistances in Parallel
Delta - Star transformation | Star - Delta Transformation
Tellegen Theorem
Thevenin Theorem and Thevenin Equivalent Voltage and Resistance
Vector Algebra | Vector Diagram
Wheatstone Bridge Circuit Theory and Principle
Vector Diagram | Three Phase Vector Diagram
Static Electric Field | Electrostatic Induction | Electric Field Strength
Joules Law of Heating
Gauss Theorem
Alkaline Batteries
Nickel Iron Batteries or Edison Batteries
Three Phase Circuit | Star and Delta System
Potentiometer Working Principle of Potentiometer
Lenz Law of Electromagnetic Induction
Seebeck Effect and Seebeck Coefficient
Faraday Law of Electromagnetic Induction
RL Series Circuit
RLC Circuit
RL Circuit Transfer Function Time Constant RL Circuit as Filter
Battery | History and Working Principle of Batteries
RL Parallel Circuit
Series RLC Circuit
Coulombs Law | Explanation Statement Formulas Principle Limitation of Coulomb’s Law
Voltage Divider
Resonance in Series RLC Circuit
Parallel RLC Circuit
Aluminum Air Battery | Experiment Reaction Equations Uses
Kelvin Bridge Circuit | Kelvin Double Bridge
Magnetic Field and Magnetic Circuit | Magnetic Materials
Biot Savart Law
What is Capacitor and Capacitance? Types of Capacitors
Zinc Carbon Battery |Types of Zinc Carbon Battery | Advantages and Disadvantages
Mercuric Oxide Battery | Chemistry Construction Advantages Uses
Variable Resistors | Defination, Uses and Types of Variable Resistors
Electric Lamp | Types of Electric Lamp
What is Inductor and Inductance | Theory of Inductor
Charging of Battery and Discharging of Battery
Magnesium Battery | Chemistry Construction of Magnesium Battery

Parallel RLC Circuit

Under Basic Electrical Engineering 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, VS. 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. parallel rlc circuit The total current, IS 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.

IS is the total source current.

IR is the current flowing through the resistor.

IC 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 IR, IC, IL 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 IR in same phase and direction to voltage. In case of capacitor, current leads the voltage by 90° so, draw IC vector leading voltage vector, V by 90°. For inductor, current vector IL lags voltage by 90° so draw IL lagging voltage vector, V by 90°. Now draw the resultant of IR, IC, IL i.e current IS at a phase angle difference of θ with respect to voltage vector, V.

vector diagram of rlc circuit

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 IR, IC, IL 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. admittance 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.

Enter your suggestion/comment here
Name : -

Email : -

Location : -

Suggestion / Comment : -