# Just started complex numbers with AC circuits

#### Asmodeus25

Joined Jul 8, 2016
6
So we just started learning complex numbers, and One of my questions I don't seem to understand how to solve and I know its pretty important. A voltage sine wave with a peak value of 300V leads another Voltage sine wave of 200V peak value by 30 degrees. calculate the RMS resultant value of these voltage waves.

#### MrAl

Joined Jun 17, 2014
8,559
Hi,

RMS means "the root of the mean of the square"
so first you square it, then find the average, then take the square root.
Try that and see what you can come up with.

#### Asmodeus25

Joined Jul 8, 2016
6
Hi,

RMS means "the root of the mean of the square"
so first you square it, then find the average, then take the square root.
Try that and see what you can come up with.
im not getting the correct answer :/

#### MrAl

Joined Jun 17, 2014
8,559
im not getting the correct answer :/

Hi,

Ok then i will do one for you for an example.

Say the voltage is 100 volts peak.
The waveform is:
Vt=100*sin(w*t)

or:
Vt=100*sin(2*pi*f*t)

Now square that and we get:
10000*sin(2*%pi*f*t)^2

now compute the mean and get:
(5000/f)/(T)

where T is the period which is T=1/f, so we get:
5000

now take the square root and we get approximately:
70.71067811865

But if you have not been taught that method yet then you just multiply by a constant factor:
100*K

and you get the right answer.
Do you know what the value of that factor K is?

#### WBahn

Joined Mar 31, 2012
26,398
So we just started learning complex numbers, and One of my questions I don't seem to understand how to solve and I know its pretty important. A voltage sine wave with a peak value of 300V leads another Voltage sine wave of 200V peak value by 30 degrees. calculate the RMS resultant value of these voltage waves.
You need to show your work. There's no way for us to help you find where you are going wrong if you don't show us what you did. We are not mind readers.

#### crutschow

Joined Mar 14, 2008
28,220

#### MrChips

Joined Oct 2, 2009
24,642
Do you know how to do vector analysis?

Since your question pertains to complex numbers, do you know how to represent 200V @ 30° phase angle in complex form?

#### Asmodeus25

Joined Jul 8, 2016
6
Hi,

Ok then i will do one for you for an example.

Say the voltage is 100 volts peak.
The waveform is:
Vt=100*sin(w*t)

or:
Vt=100*sin(2*pi*f*t)

Now square that and we get:
10000*sin(2*%pi*f*t)^2

now compute the mean and get:
(5000/f)/(T)

where T is the period which is T=1/f, so we get:
5000

now take the square root and we get approximately:
70.71067811865

But if you have not been taught that method yet then you just multiply by a constant factor:
100*K

and you get the right answer.
Do you know what the value of that factor K is?
I did this for both of them, but the answer in the text book is 280V and the rms of 100 and 200 is not even close to them. We havent used K factor yet

#### Asmodeus25

Joined Jul 8, 2016
6

#### WBahn

Joined Mar 31, 2012
26,398
I did this for both of them, but the answer in the text book is 280V and the rms of 100 and 200 is not even close to them. We havent used K factor yet

We are NOT mind readers. How can we possibly help you figure out what you did wrong when you refuse to show us what you did at all?

#### Asmodeus25

Joined Jul 8, 2016
6
Do you know how to do vector analysis?

Since your question pertains to complex numbers, do you know how to represent 200V @ 30 phase angle in complex form?
Yes, I think so, in polar its 200 V *angle sign* 45 degrees and the other is 100 *angle sign* 0 degrees. And I can then convert those to rectangular form and add them, and convert the rms, but the result isn't the answer that the textbook is giving me of 280 V.

#### Asmodeus25

Joined Jul 8, 2016
6
Yes, I think so, in polar its 200 V *angle sign* 45 degrees and the other is 100 *angle sign* 0 degrees. And I can then convert those to rectangular form and add them, and convert the rms, but the result isn't the answer that the textbook is giving me of 280 V.
I figured out where I went wrong, after doing this, I apologize for the lack of work showing, this is the first time i'm using these forums. thanks everyone for the help

#### MrChips

Joined Oct 2, 2009
24,642
I figured out where I went wrong, after doing this, I apologize for the lack of work showing, this is the first time i'm using these forums. thanks everyone for the help
Remember, forums are not only about helping yourself.
There is an audience and other people can learn from your mistakes.

#### WBahn

Joined Mar 31, 2012
26,398
Yes, I think so, in polar its 200 V *angle sign* 45 degrees and the other is 100 *angle sign* 0 degrees. And I can then convert those to rectangular form and add them, and convert the rms, but the result isn't the answer that the textbook is giving me of 280 V.
Huh?

So we just started learning complex numbers, and One of my questions I don't seem to understand how to solve and I know its pretty important. A voltage sine wave with a peak value of 300V leads another Voltage sine wave of 200V peak value by 30 degrees. calculate the RMS resultant value of these voltage waves.
How are you getting 200 V and 100 V from this problem statement?

How are you getting an angle of 45 degrees for the 200 V signal and 0 degrees for the 100 V signal?

Why won't you show your work?

What are the time-domain representations for a voltage waveform that has an amplitude of 300 V and that leads another voltage waveform that has an amplitude of 200 V at an angle of 30°.

What are the phasor representations for these two waveforms?

#### KL7AJ

Joined Nov 4, 2008
2,229
So we just started learning complex numbers, and One of my questions I don't seem to understand how to solve and I know its pretty important. A voltage sine wave with a peak value of 300V leads another Voltage sine wave of 200V peak value by 30 degrees. calculate the RMS resultant value of these voltage waves.
You will never regret getting a good understanding of complex numbers. They are applicable in EVERY field of science, and they open up whole new levels of understanding. Take the time to understand and appreciate them. Blessings on your journey.

#### MrChips

Joined Oct 2, 2009
24,642
300V pk added to 200V pk = 500V pk = 350Vrms.

Hence the textbook answer has to be less than 350V rms.
I have yet to work out the correct answer.

#### MrAl

Joined Jun 17, 2014
8,559
Hi,

I did this using both complex numbers and time domain expressions for the two waveforms and both times i get a number extremely close to:
342vrms

This should be more accurate than a simulation would show unless maybe the time step was very very tiny.

#### MrChips

Joined Oct 2, 2009
24,642
That is close enough. My answer by calculation is 341V rms depending on where I do my rounding.

If you want exact numbers I can provide it.

#### crutschow

Joined Mar 14, 2008
28,220
This should be more accurate than a simulation would show unless maybe the time step was very very tiny.
Yes, timestep does slightly affect the results.
With a maximum timestep of 0.1μs, the simulated voltage was 341.99Vrms (close enough for government work ). 