AC Parallel Circuits

Resistance, Inductance and Capacitance in AC Parallel

The following figure shows resistance, inductance and capacitance connected in an AC parallel circuit.

FIGURE

The following is the phasor diagram that shows that voltage is the reference phasor that is common to all components in a parallel circuit. The current in the capacitor (I_C) leads the voltage by 90^o and the current in the inductor (I_L) lags by an angle less than 90^o due to the resistance.

FIGURE

Impedance: At resonance, a parallel circuit is called as a rejector circuit as the impedance of the circuit is at its maximum. This impedance is called as the dynamic impedance (Z_D) and is calculated using the following formula.

Resonance: The capacitor gets charged and discharged through the inductor thus circulating a current between the two components. Now the circuit is a parallel resonant circuit. But top-up is necessary to keep the current circulating as the inductor has resistance that leads to power loss. At resonance, the current drawn from the supply is small resulting in high impedance. The resonance occurs at a certain frequency, known as resonant frequency (f₀), which is shown in the graph below.

FIGURE

        If the resistive losses are small, the same formula as for a series resonant circuit is applied. Otherwise, the resonant frequency in a parallel circuit is calculated using the following formula.