rms and average value pdf

Rms And Average Value Pdf

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These AC circuits series has taken us on a journey which has seen us discuss what AC really is all about, how its generated , some histories, concepts behind AC, its waveform, characteristics and some properties. Today we will be going over some terms and quantities associated with the Alternating Current. One of the key properties of an AC waveform, asides frequency and period, is the Amplitude which represents the maximum value of an alternating waveform or as better known, the peak value.

RMS Power vs. Average Power

So far we know that AC voltage alternates in polarity and AC current alternates in direction. However, we encounter a measurement problem if we try to express how large or small an AC quantity is. With DC, where quantities of voltage and current are generally stable, we have little trouble expressing how much voltage or current we have in any part of a circuit. One way to express the intensity, or magnitude also called the amplitude , of an AC quantity is to measure its peak height on a waveform graph. This is known as the peak or crest value of an AC waveform : Figure below. Another way is to measure the total height between opposite peaks. Unfortunately, either one of these expressions of waveform amplitude can be misleading when comparing two different types of waves.

Root mean square

Table of Contents. AC and DC Currents. It is known that the polarity of DC voltage and direction of DC current are always same i. In other words, alternating current AC is a type of current which flows first in one direction and secondly, it flows in the opposite direction. In each cycle, it changes the value from zero to the maximum and again hit the zero value.

RMS Value, Average Value, Peak Value, Peak Factor And Form Factor in AC

Definition: The maximum value attained by an alternating quantity during one cycle is called its P eak value. It is also known as the maximum value or amplitude or crest value. The sinusoidal alternating quantity obtains its peak value at 90 degrees as shown in the figure below. The peak values of alternating voltage and current is represented by E m and I m respectively.

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In other words, the averaging of all the instantaneous values along time axis with time being one full period, T. For a periodic waveform, the area above the horizontal axis is positive while the area below the horizontal axis is negative. The result is that the average or mean value of a symmetrical alternating quantity is therefore zero, 0 because the area above the horizontal axis the positive half cycle is the same as the area below the axis the negative half cycle and thus cancel each other out. This is because when we do the maths of the two areas, the negative area cancels out the positive area producing zero average voltage.

Measurements of AC Magnitude

In mathematics and its applications, the root mean square RMS or rms is defined as the square root of the mean square the arithmetic mean of the squares of a set of numbers. RMS can also be defined for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current , RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory , the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. The RMS value of a set of values or a continuous-time waveform is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform. In physics, the RMS current value can also be defined as the "value of the direct current that dissipates the same power in a resistor. The RMS value of a continuous function or signal can be approximated by taking the RMS of a sample consisting of equally spaced observations.

The Web This site. A wave form is a graph showing the variation, usually of voltage or current, against time. The horizontal axis shows the passing of time, progressing from left to right.


If, on the other hand, the voltage (current) function grows without bound over time​, the average value is dependent on the measurement interval and will not.


The Study of Root Mean Square (RMS) Value

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1 comments

Bernd G.

The mean value of a time-varying function is defined in terms of an integral. An associated quantity is the root-mean-square (r.m.s). For example, the r.m.s. value​.

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