# Instantaneous value of sinusoidal voltage

eximius
I'm just looking for some sources that would help me deduce values from the instantaneous value of a sinusoidal voltage. For example I have a question that states it as:

v = 50cos(100*pi*t - (pi/3))

I just need some material to help me deduce things such as the following:

* the peak to peak value of v (with two "^" on top)
* the RMS value of v
* mean or average value Von
* the period T

etc

Thanks.

ssana
Dear eximius,
Normally we recieve 220Volts in the residence. Here 220V is the RMS(Root Mean Square) value. Approximately 311Volts peak value and 622Volts peak to peak value.
Peak Value(in volts) = RMS value(in volts) x square root of 2.
Peak to Peak Value(in volts) = 2 X Peak Value(in volts)

Example:
Peak Value(in volts) = 220V x 1.414 = 311V
Peak to Peak Value(in volts) = 2 x 311 = 622V
Our Voltmeter reads RMS value. Therefore we are getting 220V on voltmeter.

And about period, we are getting normally 50Hz frequency in residence. This means total 50 cycles of alternate waves in one second.
Period of one wave will be = 1/50 = 0.02 Seconds

Mentor
I'm just looking for some sources that would help me deduce values from the instantaneous value of a sinusoidal voltage. For example I have a question that states it as:

v = 50cos(100*pi*t - (pi/3))

I just need some material to help me deduce things such as the following:

* the peak to peak value of v (with two "^" on top)
* the RMS value of v
* mean or average value Von
* the period T

etc

Thanks.

http://en.wikipedia.org/wiki/Sinusoid

Now can you tell us the answers to those questions?

eximius
Thanks for the help guys. Not checking wikipedia was just plain stupid of me. But please don't think I was simply being lazy and asking, I had already checked a book I have which is meant to be specific to the course... and searched google quite a bit. I only asked because I hadn't managed to find the answers.

Vpeak = 50 V ,because the 50 is equal to A, which is the amplitude
Vp2p = 100 V ,because amplitude x 2
Vrms = 35.36 V ,because Vpeak = RMS x 2^0.5
Von = unsure about this one, don't know what it is really, the average of the AC voltage would be zero but I don't see how this would help
T =

ω = 2*pi*f
ω = 100*pi
.:. 100*pi = 2*pi*f
f = 50 Hz

T = 1/f
T = 1/50
T = 0.02s

Sorry for turning this into a sort of question thread, seems to be in the wrong forum now. If a mod feels that this is the case, could they please move it to the correct forum.

Mentor
Thanks for the help guys. Not checking wikipedia was just plain stupid of me. But please don't think I was simply being lazy and asking, I had already checked a book I have which is meant to be specific to the course... and searched google quite a bit. I only asked because I hadn't managed to find the answers.

Vpeak = 50 V ,because the 50 is equal to A, which is the amplitude
Vp2p = 100 V ,because amplitude x 2
Vrms = 35.36 V ,because Vpeak = RMS x 2^0.5
Von = unsure about this one, don't know what it is really, the average of the AC voltage would be zero but I don't see how this would help
T =

ω = 2*pi*f
ω = 100*pi
.:. 100*pi = 2*pi*f
f = 50 Hz

T = 1/f
T = 1/50
T = 0.02s

Sorry for turning this into a sort of question thread, seems to be in the wrong forum now. If a mod feels that this is the case, could they please move it to the correct forum.

Looks good to me. And yes, the average value of that sinusoid is zero. It would be possible to add a DC term to it, in which case the average would not be zero:

v(t) = Vo + Acos(wt)

I'll go ahead and move this thread to the HH/Engineering forum. Good job!

eximius
Thanks again. But what exactly is Von? Not exactly an easy term to google seeing as I only get german results... :P

Edit: Oops. Just checked the digital version rather than the photocopied version I have. It's Vav not Von. Makes much more sense now.

Can't thank you guys enough. The help was very much appreciated.

Mentor
Thanks again. But what exactly is Von? Not exactly an easy term to google seeing as I only get german results... :P

I don't know, actually. I've never seen that term used for an average value. Is it really shown as Von, or some other way? Is "on" two letters in the subscript? I'd guess the "n" is for nominal, and maybe Vo is the output voltage or something?