Parallel RLC Circuit

PARALLEL RLC CIRCUIT

The circuit shows the three impedance Z₁, Z₂ and Z₃  in parallel with the supply.

The currents are given by:

where Y stands for the reciprocal of impedance Y is called the admittance and its unit is Siemen.

The admittance Y of a circuit is like that impedance, a complex quantity (with real and imaginary parts or a magnitude and phase angle).

The real part of Y is called conductance G

and imaginary part is called susceptance B.

Complex Power

The apparent power can be expressed in complex form:

S=P+jQ.

The apparent power Q, S in complex form is equal to the product of phasor voltage and conjugate of phasor current. It is known as complex power:

S=P+jQ=V x I^*

where Real power P = in phase component.

Reactive power Q = Quadrature component

V = Phasor voltage in complex form

I^* = Conjugate of phasor current in complex forms.