Respuesta :
-- The RMS value of an AC waveform is (1/2)(√2) x (peak value)
So the peak value is (√2) x (RMS value)
-- The Average value of an AC waveform is (2/π) x (peak value)
So the peak value is (π/2) x (Average value).
-- So far, this is all very entertaining, but how does it help us answer the question.
Well, we found the peak value in terms of the RMS and in terms of the Average. So we can set these equal to each other, and solve for the Average in terms of the RMS. This sounds like such a good plan, I think I'll do it !
Peak = (√2) x (RMS value) and Peak also = (π/2) x (Average value).
So (√2) · RMS = (π/2) · Average .
Divide each side by π : (√2) · RMS / π = (1/2) · Average
Multiply each side by 2 : Average = (2/π) · (√2) · RMS .
You said that the RMS value is 80 V, so
Average = (2/π) · (√2) · (80)
Average = (2 · √2 / π) · (80)
Average = 160√2 / π
Average = 72 volts . (But be sure to read the 'gotcha' below.)
Now I'll go ahead and tell you the 'gotcha':
All of these numbers are true, as far as they go. But the 'average' is only true for 1/2 cycle of an AC wave. Picture an AC wave in your mind. You'll see that it spends just as much time being negative as it spends being positive. So the 'average' of any number of AC whole cycles is zero.
The circuit's average voltage is 88.85 volts.
To find the circuit's average voltage the value given is, 80 VAC.
What is RMS voltage? How circuit's average voltage is calculated?
RMS value of a every waveform will be equal to the DC equivalent voltage. In the AC circuit , the value of the steady current which generate the same amount of heat in a given resistance in a given time and also maintains the same amount of heat at the same time.
The average value of sine wave will be zero. As the wave will be covered as half cycle with positive and half with the negative, so that they get cancel to each other and as for that we have to consider only the positive wave cycle.
The average voltage can be said as “the quotient of the area under the waveform with respect to time”.
V avg = 2√2/π * V rms
when we consider peak to peak voltage,
Vrms = 1.1107 * Vavg
so,
V rms = 1.1107 * 80
= 88.85 volts.
The circuit's average voltage is 88.85 volts.
Learn more about average voltage,
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