Parallel RLC Circuit Resonance:

Parallel RLC Circuit Resonance – Basically, parallel resonance occurs when XC = XL. The frequency at which resonance occurs is called the resonant frequency. When XC = XL, the two branch currents are equal in magnitude and 180° out of phase with each other. Therefore, the two currents cancel each other out, and the total current is zero. Consider the circuit shown in Fig. 8.11.

Parallel RLC Circuit Resonance

The condition for resonance occurs when XL = XC.

In Fig. 8.11, the total admittance

Parallel RLC Circuit Resonance

At resonance the susceptance part becomes zero

The condition for resonant frequency is given by Eq. 8.16. As a special case, if RL = RC, then Eq. 8.16 becomes


Parallel RLC Circuit Resonance

Resonant Frequency for a Tank Circuit:

The Parallel RLC Circuit Resonance is generally called a tank circuit because of the fact that the circuit stores energy in the magnetic field of the coil and in the electric field of the capacitor. The stored energy is transferred back and forth between the capacitor and coil and vice-versa. The tank circuit is shown in Fig. 8.13. The circuit is said to be in resonant condition when the suscep­tance part of admittance is zero.

Resonant Frequency for a Tank Circuit

The total admittance is

Simplifying Eq. 8.17, we have

Parallel RLC Circuit Resonance

To satisfy the condition for resonance, the susceptance part is zero.

Parallel RLC Circuit Resonance

From Eq. 8.19, we get

The resonant frequency for the tank circuit is

Parallel RLC Circuit Resonance

Variation of Impedance with Frequency:

The impedance of a Parallel RLC Circuit Resonance is maximum at the resonant frequency and decreases at lower and higher frequencies as shown in Fig. 8.15.

Variation of Impedance with Frequency

At very low frequencies, XL is very small and XC is very large, so the total impedance is essentially inductive. As the frequency increases, the impedance also increases, and the inductive reac­tance dominates until the resonant frequency is reached. At this point XL = XC and the impedance is at its maximum. As the frequency goes above resonance, capacitive reactance dominates and the impedance decreases.