In this article we will discuss how to determine effective value of alternating current and EMF, explained with the help of a suitable graph.

In a graph plot the instantaneous values of current along the ordinate and the corresponding angular displacements along the abscissa for one complete cycle or 360°. A Sine curve will be obtained as shown in figure 21.

Now plot the square curve. This is done by plotting a number of points a such that ac = (bc)^{2} and drawing a smooth curve through them.

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**The average height of this square curve gives the mean value if i ^{2} which is determined as follows: **

Let I_{m} be the maximum value of the current. Then maximum height of the square curve is I^{2}_{m}. Draw a horizontal line pq at a height of I^{2}_{m}/2 above the horizontal axis OS. The area of the rectangle opqs will be equal to the area bounded by the square curve which is shown by the shaded portions in fig. 21.

Thus, it is seen that if an alternating current is sinusoidal, its R.M.S. value is 0.707 times its maximum value.

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**Similarly, R.M.S. value of a sinusoidal e.m.f.:**

where E_{m} is the maximum value of e.m.f.