English
RFQ

Download the app

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.

Topics

Basic Physics Articles

Edwiin

Hello，I'm Wdwiin. A decade of hands-on experience in electrical engineering, specializing in high-voltage systems, smart grids, and renewable energy technologies. Passionate about technical exchange and knowledge sharing, committed to interpreting industry trends with professional insights to empower peers. Connection creates value—let’s explore the boundless possibilities of the electrical world together!

Working Voltage in Power System

Working Voltage in Power System

Working VoltageThe term "working voltage" refers to the maximum voltage that a device can withstand without sustaining damage or burning out, while ensuring the reliability, safety, and proper operation of both the device and associated circuits.For long-distance power transmission, the use of high voltage is advantageous. In AC systems, maintaining a load power factor as close to unity as possible is also economically necessary. Practically, heavy currents are more challenging to handle than hi

Frequency division method for measuring grid-to-ground insulation parameters

Frequency division method for measuring grid-to-ground insulation parameters

The frequency division method enables the measurement of grid-to-ground parameters by injecting a current signal of a different frequency into the open delta side of the potential transformer (PT).This method is applicable to ungrounded systems; however, when measuring the grid-to-ground parameters of a system where the neutral point is grounded via an arc suppression coil, the arc suppression coil must be disconnected from operation beforehand. Its measurement principle is shown in Figure 1.As

The insulation parameters of the power grid to ground are measured by the tuning method

The insulation parameters of the power grid to ground are measured by the tuning method

The tuning method is suitable for measuring the ground parameters of systems where the neutral point is grounded via an arc suppression coil, but not applicable to ungrounded neutral point systems. Its measurement principle involves injecting a current signal with continuously varying frequency from the secondary side of the Potential Transformer (PT), measuring the returned voltage signal, and identifying the system's resonant frequency.During the frequency sweeping process, each injected heter

Effect of Transition Resistance at the Grounding Point on the Rising Speed of Zero - sequence Voltage

Effect of Transition Resistance at the Grounding Point on the Rising Speed of Zero - sequence Voltage

In an arc - suppression coil grounding system, the rising speed of the zero - sequence voltage is greatly affected by the value of the transition resistance at the grounding point. The larger the transition resistance at the grounding point, the slower the rising speed of the zero - sequence voltage.In an ungrounded system, the transition resistance at the grounding point has basically no impact on the rising speed of the zero - sequence voltage.Simulation Analysis: Arc - suppression Coil Ground

Source professional electrical partners, experts, and explore smart grid & energy solutions.