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Phasor Method for Solving Parallel Circuits

Edwiin

05/30/2025

When dealing with parallel circuits, multiple branches are connected in parallel. Each branch contains components such as resistors, inductors, and capacitors, forming a series circuit within that branch. Each branch is first analyzed separately as a series circuit, and then the effects of all branches are combined.

In circuit calculations, both the magnitude and phase angle of current and voltage are taken into account. When solving the circuit, the magnitudes and phase angles of voltages and currents are considered. There are mainly three methods for solving parallel AC circuits, as follows:

Phasor Method (or Vector Method)
Admittance Method
Phasor Algebra Method (also known as Symbolic Method or J Method)

The method that provides a quick result is typically chosen. In this article, the Phasor Method will be explained in detail.

Steps to Solve Parallel Circuits Using the Phasor Method

Consider the following circuit diagram to solve the circuit step - by - step.

Step 1 – Draw the Circuit Diagram

First, sketch the circuit diagram according to the problem. Take the above circuit as an example, which features two parallel branches:

Branch 1: Resistance (R) and inductance (L) in series
Branch 2: Resistance (R) and capacitance (C) in series
The supply voltage is denoted as V volts.

Step 2 – Calculate Impedance for Each Branch

Determine the impedance of each branch separately:

Step 3 – Determine the magnitude of current and phase angle with the voltage in each branch.

Here,

ϕ1 is a lagging angle, indicating an inductive load.
ϕ2 is a leading angle, characteristic of a capacitive load.

Step 4 – Construct the Phasor Diagram

Take the supply voltage as the reference phasor and draw the phasor diagram, plotting the branch currents as shown below:

Step 5 – Compute the Phasor Sum of Branch Currents

Calculate the phasor sum of the branch currents using the component method:

And therefore, current I will be

Step 6 – Find the phase angle ϕ between the total current I and the circuit voltage V.

Here angle ϕ will be lagging as I_yy is negative

The power factor of the circuit will be Cosϕ or

This is all about the phasor method of solving parallel circuits.

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