Hi friends ...

I have a question as attached photo1 below

and i want to make sure about my solution as photo2 below .
Is it correct??

really i misunderstanding with using average and rms values ..
please anyone can help me to know what are the differences among the following forms and when can i use them ...
R1 = Vrms/i2
R1 = Vaverage/i2 = Vdc/i2
R1 = Vpeak/i2

thank you in advance

 

Vpeak is just the maximum amplitude of the sinewave. It is used in conjunction with the current at that point to compute the instantaneous power at that one point.
Vaverage for a sinewave is zero and is not of much use in AC waveforms involving sines and cosines.
Vrms is the square root of the average of the squared voltage over one cycle of the AC wavforms.

Vrms * Irms gives the average power
http://en.wikipedia.org/wiki/Root_mean_square

 

I may be missing something, but any firing angle greater than 90 degrees for a true sine wave would leave the SCR reverse biased and unable to turn on. This leads me to believe that this voltage is a rectified waveform, but I would need your confirmation of that.

As far as your question about differences between Vrms, Vaverage, and Vpeak:

Vrms is your equivalent DC voltage of a waveform in terms of power generated. From wikipedia: "the RMS value of a periodic current is equal to the DC current that delivers the same average power to a resistor as the periodic current." When it comes to power delivered, your RMS voltage can be treated as a DC voltage for calculation purposes, which makes it handy. For sinusoidal waveforms, this is your go to voltage value, hence why it is so popular when it comes to power distribution.

Vpeak is your maximum voltage (in this example, 120V). This value has merit when it comes time to determine maximum component requirements, such as the voltage rating of a filter capacitor. It is used less frequently than Vrms or Vaverage.

Vaverage is the average of the instantaneous voltages of your waveform, or the integral of your voltage waveform. For a sinusoidal waveform, this would be zero if an integral were used directly over the full period, so you would take the integral over a quarter of the period. This value is useful for waveforms that do not have a negative going portion, like a rectified waveform.

This site shows a mathmatical comparison of Vrms and Vaverage side-by-side: http://www.rfcafe.com/references/electrical/sinewave-voltage-conversion.htm

TL;DR: Vrms for sinusoids, Vpeak for component ratings, Vaverage for non-sinusoids

EDIT: Vpeak is also used for instantaneous power calculations, as noted above by PapaBravo.

 

Peak voltage is the maximum voltage. If the signal is sine wave, the peak voltage equals the sine wave amplitude.

Average voltage is the average over a duration of time and is equal to the DC voltage. The average voltage of a symmetrical sine wave signal is zero.

RMS value is related to the power or heating effect of the signal.
The RMS value of any signal is the equivalent constant DC voltage that will produce the same heating effect as the given signal.

120VAC mains voltage is the RMS voltage.
The amplitude = peak = 120 x 1.414 = 170V

 

Thank you all for new info...
Now ,, I solved my question
Pav=Pdc =1/2pi* int(from 102.9 to 180)of(120sinwt).dwt =14.99watt
then R= P/I2 =56.69 kohm Its correct or not??

 

Why not simply calculate V at 102.9°?

i.e. V = 170 sin(102.9 x pi/180)

 

i need to calculate the value of R and i have the current value through it is 15mA,
and the voltage across R is the same voltage after firing SCR
thus Vav= 1/2pi integration(from 102.9 to 180)of(170sinwt).dwt HERE my problem ?? (Find Vav or Vrms and how i can know or assumed that )
then R=Vav/I