Topic 2.4.1 Root Mean Square RMS Voltage

Topic 2.4.1 – Root Mean Square – RMS Voltage.

Learning Objectives:

At the end of this topic you will be able to;

apply the formula for a sinusoidal AC voltage;

Root Mean Square (RMS) Voltage.

In topic 2.4 we are going to be investigating some different methods of constructing simple power supplies that would enable projects to be run from the mains supply.

Such a simple statement actually introduces a number of issues, which need to be addressed:

Firstly the mains electricity is an alternating current supplied at 240V. You might expect the graph to look like the following.

In reality if you were to display the mains voltage on an oscilloscope you would obtain a quite different and possibly surprising result as shown below:

The reason for this is that the value of 240V a.c. refers to a voltage called the root mean square(or rms) voltage. The root mean square voltage of an a.c. signal is the value of a sinusoidal a.c. voltage which would provide the same heating effect in a resistor as the equivalent d.c. voltage. So in this case a 240V a.c. voltage provides the same heating effect in a resistor as a 240V d.c. voltage.

For a sinusoidal voltage it is always worth remembering that the peak value of the voltage will always be higher than the rms voltage. The calculation of the rms voltage or peak value for a sinusoidal wave is quite straightforward as shown by the following equations.

In our dealings with power supplies in the exam we will have to calculate one of these values, and sketch the graph of the resulting a.c. waveform, labelling the value of the peak voltage. We will see more of the graphs in the next section of these notes when we deal with the second issue with power supplies which is that electronic circuits only work with d.c. We therefore have to find a way to change a.c. into d.c. but more of that later. For now we will just concentrate on calculating rms and peak values.

Examples:

1.A sinusoidal voltage source has a peak value of 14V, determine the rms voltage of this supply.

In this case we need to find the rms voltage so we use the formula:

2.An a.c. power supply has an rms voltage of 6V. What is the peak voltage from the power supply.

In this case we need to find the peak voltage so we use the formula:

Now it’s time for you to have a go:

Student Exercise 1:

1.A sinusoidal voltage source has a peak value of 20V, determine the rms voltage of this supply.

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2.An a.c. power supply has an rms voltage of 9V. What is the peak voltage from the power supply.

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3.An a.c. power supply has an rms voltage of 12V. What is the peak voltage from the power supply.

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4.A sinusoidal voltage source has a peak value of 31.1V, determine the rms voltage of this supply.

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5.An a.c. power supply has an rms voltage of 120V. What is the peak voltage from the power supply.

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Solutions to Student Exercise.

No examination style questions have been set in this topic as they are integral to longer questions on power supplies, which we are not yet in a position to answer, so time to move on to topic 2.4.2 – Rectification.

Self Evaluation Review

Learning Objectives / My personal review of these objectives:
 /  / 
apply the formula for a sinusoidal AC voltage

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