• Skip to main content
  • Skip to primary sidebar
  • Basic Electronics
  • Digital Electronics
  • Electronics Instrumentation
  • ADC
  • Comparisons

Electronics Coach

All About Electronics

Phase Difference in AC Circuits

Phase Difference is defined as the delay between two or more alternating quantities while attaining the maxima or zero-crossings giving rise to the difference in their phases. This difference in two waves is measured in degrees or radians and is also known as phase shift.

It is sometimes defined as the difference between two or more sinusoidal waveforms in consideration with a reference axis. It is denoted by φ and corresponds to the shift in the waveform along the horizontal axis from a common reference point.

We will discuss the phase difference of AC circuits in detail later first let us understand-

What is Phase?

The phase of alternating quantities is defined in terms of displacement and time period. In terms of displacement, phase represents the angle from a reference point by which the phasor representing the alternating quantity travels up to the point of consideration.

To understand this, have a look at the figure given below:

concept of phase

In the above figure, the x-axis is the reference axis and at instant A, the phase φ of the alternating quantity is 0⁰ while under displacement, the phase of the same quantity at instant B represents the angle (in degrees or radians) through which the phasor has traveled considering the same reference axis i.e., x-axis. Generally, the phase of the alternating quantity varies from 0 to 2π in rad or 0⁰ to 360⁰.

Furthermore, in terms of the time period, the phase at any particular instant is defined as the fraction of the time period through which it is advanced with respect to the reference instant. Consider the waveform representation given below:

representation of phase

Here 0 is considered as the reference instant, thus, the phase of the alternating quantity at A is T/4 while at B is 3T/4.

Concept of Phase Difference in AC Circuits

Suppose a comparison between 2 alternating quantities is made according to the overlapping of their peaks and zero crossings.

So, when the peak and zero crossings of alternating quantities with same frequency coincide then such quantities are said to be in phase. More simply, we can say, that, when two alternating quantities of same frequency reach their maximum positive, negative, and zero values at the same instant of time during one complete cycle irrespective of their amplitude then such quantities are said to have a similar phase. This explanation is clearly shown in the figure given below:

inphase relationship of sine waves

Conversely, when the peak and zero crossing of the alternating quantities with same frequency do not coincide then these quantities are said to be out of phase with respect to each other and a specific difference in the phase exists between the two. In a nutshell, we can say, when two alternating quantities of the same frequency attain their positive and negative peaks and zero values at different time instants in one complete cycle, considering the same reference axis, then there exists a phase difference between them. The out of phase relationship between two alternating quantities is clearly shown in the figure below:

out of phase relationship of sine waves

Equation for Phase Difference

The general equation of the alternating quantities is given as:

phase difference equation for alternating quantities

: φ represents the phase of the alternating quantity,

Am is the amplitude of the waveform,

ωt represents the angular frequency of the waveform.

Here the φ can be either positive or negative.

Now, the question arises, when φ is positive, and when it is negative?

Before understanding positive and negative phase shifts, understand the condition for zero phase difference.

So, when the phase of the alternating quantity is 0 then the instantaneous value of the sinusoidal quantity is at t = 0 which is considered as reference. The figure given below indicates φ = 0⁰.

condition of no phase difference

Positive Phase Shift: When an alternating quantity begins before t=0 which is considered as reference, then the positive slope of the alternating quantity is shifted towards the left thereby crossing the horizontal axis before the reference. Thus, in such a case, φ>0 and the angle will be positive in nature. This gives rise to a leading phase angle.

This can be said conversely as, in the case of a positive phase, the alternating quantity has some positive instantaneous value at t = 0. This is clearly shown below:

condition for positive phase difference

In the below-given figure, one is the voltage waveform which is started before the reference point and the other is the current waveform which exactly starts at t=0 i.e., reference. Generally, in a purely inductive circuit, voltage leads the current.

condition for posiitve phase difference for V and I waveforms

Here the current is lagging voltage by angle φ.

Negative Phase Shift: When the alternating quantity starts after t=0 i.e., reference point, then its positive slope is shifted towards the right and so crosses the horizontal axis after the reference point. Therefore, here φ<0, and the angle will be negative in nature. When the phase angle is negative then it represents a lagging phase angle.

For the negative phase, the alternating quantity has some negative instantaneous value at t = 0, as represented here:

condition for negative phase difference

In the figure given below, we have current and voltage waveforms, and it is clearly shown that the voltage waveform is started after the reference and the current waveform is started exactly at the reference. Generally, in purely capacitive circuits, current leads the voltage.

condition for negative phase difference for V and I waveforms

Here voltage is lagging current by angle φ.

The relationship between voltage and current sinusoidal waveforms is very important while dealing with AC circuits as these form the base of AC Circuit analysis.

Related Terms:

  1. Clipper Circuits
  2. Phase Modulation (PM)
  3. Zero Crossing Detector
  4. Phase-Locked Loops (PLL)
  5. Phase Shift Oscillator

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Most Searched Terms

  • Difference Between Half Wave and Full Wave Rectifier
  • Sample and Hold Circuit
  • Full Wave Rectifier
  • Difference between LED and LASER
  • Characteristics of JFET
  • Varactor Diode
  • 3 Phase Rectifier
  • Number System
  • Difference Between Clipper and Clamper
  • Analogous Systems

Trending Terms

  • Difference Between LED and OLED
  • AC Servomotor
  • Pulse Code Modulation (PCM)
  • Difference Between Multiplexer (MUX) and Demultiplexer (DEMUX)
  • Peak Detector
  • Time Division Multiplexing (TDM)
  • Difference between RC and RL Circuit
  • Differential Amplifier

New Additions

  • Resonant Converters
  • AC Voltage Controllers
  • Static Circuit Breakers
  • Synchronous Motor Drives
  • DC Drives

Categories

  • Analog & Digital Communication
  • Basic Electronics
  • Comparisons
  • Control Systems
  • Digital Electronics
  • Electronics Instrumentation
  • Optical Fiber System
  • Power Electronics

Copyright © 2025 · Electronics Coach · Contact Us · About Us · Privacy