RMS Value of Alternating Current

When the flow of charge changes directions at regular intervals, it constitutes an alternating current. In an alternating current, along with the direction of the current, the voltage level also gets reversed. An AC produces positive and negative values of the same magnitude. AC is used widely in generating power for houses, office buildings, etc.

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The alternating current follows a sinusoidal curve where its voltage increases at a steady rate from zero to the positive peak voltage. The voltage then reverses and drops to zero, and then goes negative till it reaches a negative peak value. The positive and negative peak values are equal in magnitude but opposite in polarity. After reaching the negative peak, the voltage reverses again to reach the zero value. This cycle repeats itself at regular intervals.

Generating Alternating Current

AC is generated using an alternator device. An alternator is an electrical generator that is designed to produce AC. The three main elements of an alternating current are

• A hot wire which transmits the power.

• A neutral that provides the reverse path to the hot wire. This is connected to the earth at the other end.

• The ground wire is the third element that is connected to the metallic parts of the equipment, which provides safety and prevents electric shock hazards.

The Average Value of Alternating Current

A sinusoidal wave’s average value is taken over its half-cycle since the two halves of a whole sinusoidal wave cancel out each other in one complete cycle. The average value of an AC is equivalent to the DC that transmits the same charge across any point of the circuit as the AC (simultaneously). To calculate the average value of AC current, we divide the positive half of the sinusoidal wave into “n” equal portions (mid-ordinates). The width of each portion is n degrees or t seconds. Each portion’s height is equal to the waveform's instantaneous value at that point along the x-axis.

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The average voltage is given by (sum of all the mid-ordinates)/(total number of sections)

In the example shown above, VAV = (V1 + V2 + V3 + …. + Vn)/12.

The Root Mean Square Value of Alternating Current

The root means the square value of any quantity is obtained by:

• Taking the squared value of the quantity over a fixed interval of time.

• Finding it's mean.

• Getting the square root of this mean.

The RMS value of AC current is also called its effective value which supplies the same electrical magnitude to a given load as an equivalent DC circuit. We can define root mean square value of alternating current in other words as “an equivalent DC value which gives you the volts or amps of DC that a sinusoidal wave (time-varying) is equal to in terms of producing the same magnitude of power.”

Let us see how to calculate the RMS value of alternating current. There are two ways of doing it; graphical or analytical. We will go through the graphical method for finding the root mean square value of AC current.

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We apply the same logic of calculating the average voltage of an AC discussed above, i.e. by dividing the positive waveform into equidistant mid-ordinates.

• Each of the mid-ordinate values is then multiplied by itself to get the squared values.

•  After that, this squared value is divided by the total number of mid-ordinates, giving us the mean value of ac current. 

• Finally, we take the square root of this value to get the alternating current RMS value.

\[V_{RMS} = \sqrt{\frac{V_{1} + V_{2} + V_{3} + . . . . + V_{n}}{\text{number of mid - ordinates}}}\]

AC Voltage

AC voltage fluctuates in a sinusoidal form with time and is given by the formula:

V = V_p* Sin2πft, where V is the voltage of AC at time t, V_p is the peak voltage, t is time, and f is the frequency in Hertz.

Characteristics of an AC Waveform

• The Time Period (t):

It is the duration of time in seconds in which the waveform repeats itself (from start to finish). It is also referred to as the waveform periodic time (for sine waves) or pulse width (for square waves).

• Frequency (f):

Frequency is the number of times a sinusoidal wave repeats itself within one second and f = 1/t. Frequency is measured in Hertz (Hz).

• Amplitude (A):

This is the intensity or magnitude of the waveform expressed in amps or volts.

Different Types of Waveforms

As long as the current and voltage are alternating, AC waves can have many forms. With an oscilloscope hooked up to a circuit which is AC, we would get many forms of the waves if we plot a graph of voltage over time, as shown below:

• Sine Wave

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• Square Wave

They are mostly used in switching and digital electronics for testing their operation.

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• Triangle Wave

These waves are found in sound synthesis and can be used to test linear electronics for example an amplifier.

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