Third , we can implement Fourier Analysis for analysis of periodic signals which has the characteristic of a sinusoidal waveform. The last , it is quite complicated to understand, but sinusoid is easy to analyze because its integral and derivative functions are also sinusoids.
After so many benefits from learning sinusoidal, do you know what mathematical theory we will use for ac circuit? The most basic of the dc circuit analysis theory such as :. You need to understand some parameters found in the ac circuit such as :. Along with dc circuit theorems for ac circuit :. Please look at the sinusoidal function of ac voltage :. The sinusoidal waveform in Figure. From two figures in Figure. We obtain. In general,.
T is different with t , where T is the time required for one cycle to complete or the number of seconds per cycle. T is also called by period. The opposite or reciprocal value of period T is the frequency f of the sinusoid, means the number of cycles per second.
From Equations. Let us see a sinusoidal wave equation ,. Both argument and phase can be in radians or degrees. There are two sinusoids,. The starting point of v 2 in Figure. From Figure. We are able to compare v 1 and v 2 in this matter because they operate with the same frequency even the amplitude is different. Below we will see how to graph sinusoidal functions. Every sinusoid waveform can be expressed in either cosine or sine form.
When comparing two sinusoids, it is wise to express in the same waveform as either cosine or sine with positive amplitudes.
This can be achieved by using the following trigonometric function:. Using these identities, it is easy to notice that. With these relationships, we can transform a sinusoid from cosine form to sine or vice versa. A graphical drawing can be used to compare or relate as an alternative approach to using the trigonometric function in Equations. Notice the set of axes in Figure. The horizontal axis refers to the magnitude of cosine and the vertical axis points down refers to the magnitude of sine.
The angle is measured by positive value in a counterclockwise direction from the horizontal axis. This calculation method can be used to compare two sinusoids. For example, we consider in Figure. This graphical method can add two sinusoids with the same frequency when one has sine waveform and the other has cosine waveform. From these posts, we will learn about AC Power Analysis:.
We will also looking for some applications such as:. After finishing the single-phase AC circuit, we will move on to analyzing the three-phase AC circuit and read a brief explanation of how does a wattmeter work. For better understanding, let us review examples below :.
Find the amplitude, phase, period, and frequency from. Solution :. State which one is leading. Solution: There are three ways to solve the problem. The net power in an AC cycle is not zero because power is a function of the square of the current.
Hence, the power is always positive except for one special case irrespective of the direction of the current. When an AC current transmits zero power, it is called wattless current. This happens when the current and voltage are exactly 90 degrees out of phase. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more.
Ask Question. Asked 4 years, 3 months ago. Active 4 years, 3 months ago. Viewed times. Improve this question. DanielSank Add a comment. Active Oldest Votes. Improve this answer. Yashas Yashas 6, 7 7 gold badges 33 33 silver badges 61 61 bronze badges. The waveform will have a countess tiny zig-zag parts because of the presence of harmonics but it is still largly sinusoidal.
The most common thing nowadays seems to be that the peaks of the cycles get clipped off known as 'flat-topping' , which I think is largely due to switched-mode power-supplies which tend to take current around the peaks only. Sign up or log in Sign up using Google. Sign up using Facebook.
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