## Resonance in parallel A.C circuits (Parallel Resonance)

An electrical circuit containing reactive elements(L and C) is said to be in resonance if the circuit power factor is unity. If it happens in a series a.c circuit (i.e R-L-C series circuit),it is called series resonance. If this condition(i.e unity p.f) occurs in a parallel a.c circuit .it is called parallel resonance. Resonance means to be in step with i.e circuit voltage and current are in phase with.s

A parallel circuit containing reactive elements( L and C) is said to be in resonance when the circuit p.f is unity i.e reactive component of line current is Zero. The frequency at which it occurs is called the resonant frequency(fr).

Parallel circuit consisting of Coil shunted by a capacitor is shown in the figure.

The phasor diagram is shown below:

The circuit will be in resonance when the reactive component of line current is Zero i.e

and can be achieved by changing the supply frequency because both Ic and IL sinΦL are frequency dependent. Resonance takes place when the reactive component of line current will be Zero and the frequency is called resonant frequency(fr).

At parallel resonance, the circuit condition is:

The resonant frequency will be in Hz if R,L and C are measured in ohms, henries and farads respectively.

## Impedance at Parallel resonance

The impedance Zr=(L/CR) at parallel resonance is known as equivalent or dynamic impedance and is the pure resistance as there is no frequency term present. At resonance the value of L/C is very large so the Zr is very high at parallel resonance.

## Line current at parallel resonance

At the parallel resonance the line current Ir is minimum and is

As the Zr is very high so Ir will be very small at parallel resonance. The small current Ir is only the amount needed to meet the resistance losses in the circuit. The parallel resonance is also called current resonance because the current circulating between the two branches of the circuit is many times greater than the line current taken from the supply.

## Q-factor of a parallel Resonant circuit

At parallel resonance, the circulating current between the two branches is many times greater than the line current. This current amplification produced by the resonance is termed as Q-factor of the parallel resonant circuit i.e

## Bandwidth of parallel Resonant circuit

The bandwidth of a parallel resonant circuit is defined as the range of frequencies over which the circuit impedance is equal to or greater than 70.7% of maximum circuit impedance(i.e Zr ,the impedance at resonance).The circuit impedance is maximum (i.e Zr) at fr while half-power points(i.e f1 and f2) occur at 0.707 Zr.

## Salient Features of parallel Resonance

- The circuit power factor is unity(i.e 1) so that parallel resonant circuit behaves as a resistance.
- Since parallel resonant circuit is resistive ,it means that:
- circuit admittance=circuit conductance
- circuit susceptance is Zero.
- The circuit impedance of a parallel resonant circuit is maximum.
- At parallel resonance ,the circuit current is minimum and is given by
- Ir=V/Zr where Zr is circuit impedance at parallel resonance.
- The resonant frequency(fr) of a parallel resonant circuit can be found by equating susceptance of the circuit at fr to Zero.

## Related terms:

## For more notes on electrical engineering:

- http://notesforengineering.com/
- http://abhinavbhattarai.com.np/2020/09/20/from-maxwells-equations-to-electrical-engineering/