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Parallel Resonance Circuit Diagram
If the resonance occurs in parallel RLC circuit, then it is called as Parallel Resonance. Consider the following parallel RLC circuit, which is represented in phasor domain.
Here, the passive elements such as resistor, inductor and capacitor are connected in parallel. This entire combination is in parallel with the input sinusoidal current source.
Write nodal equation at node P.
−I + IR + IL + IC = 0
Equation 1
The above equation is in the form of I = VY.
Therefore, the admittance Y of parallel RLC circuit will be
Parameters & Electrical Quantities at Resonance
Now, let us derive the values of parameters and electrical quantities at resonance of parallel RLC circuit one by one.
Resonant Frequency
We know that the resonant frequency, fr is the frequency at which, resonance occurs. In parallel RLC circuit resonance occurs, when the imaginary term of admittance, Y is zero. i.e., the value of 
should be equal to zero
⇒ XL = XC
The above resonance condition is same as that of series RLC circuit. So, the resonant frequency, fr will be same in both series RLC circuit and parallel RLC circuit.
Therefore, the resonant frequency, fr of parallel RLC circuit is
Where,
- L is the inductance of an inductor.
- C is the capacitance of a capacitor.
The resonant frequency, fr of parallel RLC circuit depends only on the inductance L and capacitance C. But, it is independent of resistance R.
Admittance
We got the admittance Y of parallel RLC circuit as
Substitute, XL = XC in the above equation.
⇒ Y = 1/R
At resonance, the admittance, Y of parallel RLC circuit is equal to the reciprocal of the resistance, R. i.e., Y = 1/R
Voltage across each Element
Substitute, 
in Equation 1
⇒ I = VR
⇒ V = IR
Therefore, the voltage across all the elements of parallel RLC circuit at resonance is V = IR.
At resonance, the admittance of parallel RLC circuit reaches to minimum value. Hence, maximum voltage is present across each element of this circuit at resonance.
Current flowing through Resistor
The current flowing through resistor is
IR = V/R
⇒ IR = I
Therefore, the current flowing through resistor at resonance is IR = I.
Current flowing through Inductor
The current flowing through inductor is
Substitute the value of V in the above equation.
⇒IL = −jQI
Therefore, the current flowing through inductor at resonance is IL = −jQI.
So, the magnitude of current flowing through inductor at resonance will be
|IL| = QI
Where, Q is the Quality factor and its value is equal to
Current flowing through Capacitor
The current flowing through capacitor is
Substitute the value of V in the above equation.
⇒ IC = jQI
Therefore, the current flowing through capacitor at resonance is IC = jQI
So, the magnitude of current flowing through capacitor at resonance will be
|IC|=QI
Where, Q is the Quality factor and its value is equal to
Note − Parallel resonance RLC circuit is called as current magnification circuit. Because, the magnitude of current flowing through inductor and capacitor is equal to Q times the input sinusoidal current I.
The document Parallel Resonance | Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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FAQs on Parallel Resonance - Network Theory (Electric Circuits) - Electrical Engineering (EE)
| 1. What is parallel resonance in electrical engineering? |  |
| 2. How does parallel resonance affect the voltage across the circuit? | |
Ans. In parallel resonance, the voltage across the circuit is maximum. This is because the impedance of the circuit is at its minimum, causing the current to be at its peak. As a result, the voltage drop across the inductor and capacitor is minimized, leading to a higher voltage across the entire circuit.
| 3. What are the applications of parallel resonance in electrical engineering? | |
Ans. Parallel resonance has various applications in electrical engineering. It is commonly used in power factor correction circuits, where it helps to compensate for reactive power and improve overall power efficiency. It is also utilized in filter circuits, where it allows for the selective passage of certain frequencies while attenuating others.
| 4. How can parallel resonance be used in wireless communication systems? | |
Ans. Parallel resonance can be employed in wireless communication systems for frequency selection and tuning. By designing the circuit to resonate at a specific frequency, it becomes highly sensitive to signals at that frequency, allowing for efficient reception and transmission. This technique is commonly used in radio and television receivers.
| 5. What are the potential drawbacks of parallel resonance in electrical circuits? | |
Ans. While parallel resonance can be advantageous, it also poses certain challenges. One drawback is the potential for high circulating currents in the circuit, which can lead to power losses and overheating. Additionally, the circuit's sensitivity to frequency variations can cause instability and affect its performance. Proper design and control measures are necessary to mitigate these issues.
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