Class 12 > Unit # 20:AC Circuits > AC through RC Series and RL Parallel Circuit

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AC Through Parallel RC, RL, RLC Circuits and Parallel Resonance

Video Lecture

Watch the complete video lecture below to understand alternating current flowing through parallel RC and RL circuits, parallel RLC circuits, and parallel resonance.

Describe the Flow of AC Through RC and RL Parallel Circuits

1. Parallel RL Circuit

"In a parallel RL circuit, the applied voltage $V$ is common to both components and is plotted in the standard reference position on the phasor diagram, while individual branch currents are determined by their respective branch reactances."

In a parallel RL circuit, a resistor ($R$) and an inductor ($L$) are connected in parallel across an alternating voltage source. The applied voltage $V$ is common across both parallel branches. Because the branch currents ($I_R$ and $I_L$) are out of phase—with the inductive current lagging behind the resistive current—phasor addition must be employed to determine the total supply current.

Using the phasor diagram and Pythagoras' theorem, the total current $I$ is given by:

$$I = \sqrt{I_R^2 + I_L^2}$$

The reciprocal of impedance ($Z$) for a parallel RL circuit is expressed as:

$$\frac{1}{Z^2} = \frac{1}{R^2} + \frac{1}{X_L^2}$$

2. Parallel RC Circuit

"Parallel RC circuits are resolved similarly to parallel RL circuits, where the current phasors $I_R$ and $I_C$ are out of phase and require phasor addition to calculate the total current."

In a parallel RC circuit, a resistor ($R$) and a capacitor ($C$) are connected in parallel across an alternating voltage source. The applied voltage $V$ is common across both branches. The current flowing through the capacitor ($I_C$) leads the resistive current ($I_R$) by $\frac{\pi}{2}$ radians.

Using phasor addition, the total current is:

$$I = \sqrt{I_R^2 + I_C^2}$$

The reciprocal of impedance ($Z$) for a parallel RC circuit is expressed as:

$$\frac{1}{Z^2} = \frac{1}{R^2} + \frac{1}{X_C^2}$$

Fig: Circuit diagrams and phasor waveforms for parallel RC and RL circuits.

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