rms value of sine wave VRMS Vpk 0 7071 20 x 0 7071 14 14V Note that this value of 14 14 volts is the same value as for the previous graphical method Then we can use either the graphical method of mid ordinates or the analytical method of calculation to find the RMS voltage or current values of a sinusoidal waveform
The RMS effective value of a sine wave of current is 1 sqrt 2 or about 0 707 times the peak value The RMS value of a sine wave voltage should be such that the average power is the product of the RMS voltage across and RMS current through the resistance of the circuit just as P VI in the equivalent DC circuit Peak values can be calculated from RMS values from the above formula which implies V P V RMS 2 assuming the source is a pure sine wave Thus the peak value of the mains voltage in the USA is about 120 2 or about 170 volts The peak to peak voltage being double this is about 340 volts
rms value of sine wave
rms value of sine wave
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Sine Wave RMS Value Derivation without Calculus Alternating
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The World Through Electricity Root Mean Square A K A RMS Value
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For AC sine wave RMS values of current and voltage are I RMS 0 707 x I M V RMS 0 707 V M To find the RMS value of a sine wave We may use the following two methods Mid Ordinate Method Integration Method Lets see how to find the R M S values of a sine wave Methods for Finding RMS Value of Sine Wave Analytical Method Method 1 When a DC offset V 0 V 0 V 0 is added to the sine wave we can determine our new RMS value with V RMS V 0 2 V p 2 2 V 0 2 V p 2 2 footnotesize begin split V text RMS sqrt V 0 2 left frac V p sqrt 2 right 2 sqrt V 0 2 frac V p 2 2 end split V RMS V 0 2 2 V p 2 V 0 2 2 V p 2
Analytical Method Graphical Method In this method we use a waveform to find the RMS value The graphical method is more useful when the signal is not symmetrical or sinusoidal The accuracy of this method depends on the number of points taken from the waveform In summation for sine waves RMS is always the peak value times 0 707 We could also say the RMS value of any sine wave is its peak divided by approximately 1 414 Again these ratios would not necessarily be true of non sine waves
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The average voltage or current of a periodic waveform whether it is a sine wave square wave or triangular waveform is the equivalent to the DC value of an alternating waveform The average or mean value is defined as the quotient of the area under the waveform with respect to time To calculate the RMS value of any function we first square it then find the mean value over some time period and finally take the square root of it Since sine and sin squared functions are both symmetrical in their centers we
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