Parallel RLC Circuit Impedance with Phasor Diagram

A parallel RLC circuit consists of the resistance, inductance, and capacitance in parallel. Like the series RLC circuit, here also when we apply a sinusoidal voltage, all the voltages and currents of the branches remain sinusoidal at the steady-state condition. The frequency of all the branch signals remains the same as the source frequency. But the amplitudes and the angles may differ in different branches.

Here in this article, we will examine the steady-state responses and behaviors of a parallel RLC circuit. For that, we draw a basic parallel RLC circuit.

parallel RLC circuit
Since we apply a sinusoidal voltage across the circuit, we can represent the expression of that voltage as

parallel RLC circuit 1

We shall also consider that the current drawn by the circuit is I.
Here we assume that the resistance R takes the current IR, the inductance takes the current IL, the capacitance takes the current IC.

Now by applying Kirchhoff’s Current Law, we get,
parallel RLC circuit 2
Where Y is the admittance of the circuit. Therefore the expression of Y is
parallel RLC circuit 3

The phase angle between the source voltage and the circuit current is
parallel RLC circuit 4

From the above expression, it is obvious that the sign and value of the angle depend on the relative value of the capacitive and inductive reactance of the parallel RLC circuit.

Here in the parallel RLC circuit another thing we have to observe. The current passing through the inductive branch legs the source voltage by exactly 90°. On the other hand, the current through the capacitor branch leads the source voltage by exactly 90°.

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