To calculate the r.m.s. value, we first need to find the root mean square of the given values. We square each value, sum them, divide by the number of values, and then take the square root of the result.
0, 5, 10, 20, 50, 60, 50, 20, 10, 5, 0, -5, -10
r.m.s. value = sqrt((0^2 + 5^2 + 10^2 + 20^2 + 50^2 + 60^2 + 50^2 + 20^2 + 10^2 + 5^2 + 0^2 + (-5)^2 + (-10)^2)/13)
= sqrt((0 + 25 + 100 + 400 + 2500 + 3600 + 2500 + 400 + 100 + 25 + 0 + 25 + 100)/13)
= sqrt(10975/13)
= sqrt(844.23)
≈ 29.06 V
Next, we calculate the peak value, which is simply the maximum value in the given list. In this case, the peak value is 60 V.
The form factor is given by the ratio of r.m.s. value to the average value. The average value is calculated by summing all the values and dividing by the number of values.
Average value = (0 + 5 + 10 + 20 + 50 + 60 + 50 + 20 + 10 + 5 + 0 + (-5) + (-10))/13
= 205/13
≈ 15.77 V
Form factor = r.m.s. value / average value
= 29.06 / 15.77
≈ 1.84
Finally, the peak factor is calculated by dividing the peak value by the r.m.s. value.
Peak factor = peak value / r.m.s. value
= 60 / 29.06
≈ 2.07
For a sine wave, the average value would be the same as the peak value divided by pi, which is approximately 3.14.
Average value of sine wave = 60 / 3.14
≈ 19.11 V
Calculate the r.m.s. value, the form factor and peak factor of a periodic voltage having the following values for equal time intervals changing suddenly from one value to the next : 0, 5, 10, 20, 50, 60, 50, 20, 10, 5, 0, −5, −10 v etc. what would be the average value of sine wave having the same peak value ?
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1 answer