# sin wav and phase angle

#### leejohnson222

Joined Jan 11, 2023
57
This one is getting me in a tangle, find Ip, f and phase angle,

I = IPsin(2pi f t - phase angle)

i have Ip = 10
to find freq i need to use 1/ time of 1 full cycle
looks to me like 1 cycle is 0.001 s
so 1/0.001 is 1000hz ?

the next part is where i cant work out phase angle, i keep watching the lecture but its not clicking

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#### StefanZe

Joined Nov 6, 2019
191
At time 0.00025 -> I=0. If you put this point into I = Ip sin(2 pi f t - phaseangle) you can calculate the phase angle.

#### WBahn

Joined Mar 31, 2012
29,507
Which points on the graph correspond to a total angle of zero?

Be sure to take into account both the value at that point, but also what direction the values are changing (i.e., increasing in value or decreasing in value).

#### MrAl

Joined Jun 17, 2014
10,906
This one is getting me in a tangle, find Ip, f and phase angle,

I = IPsin(2pi f t - phase angle)

i have Ip = 10
to find freq i need to use 1/ time of 1 full cycle
looks to me like 1 cycle is 0.001 s
so 1/0.001 is 1000hz ?

the next part is where i cant work out phase angle, i keep watching the lecture but its not clicking
Hi,

Another thing that may help you visualize this is to draw a second sine wave of the same frequency and amplitude but with zero phase shift, along with your original sine wave. That means sin(wt+ph) where ph=0. Draw that and see if you can figure it out.

#### leejohnson222

Joined Jan 11, 2023
57
i think the sin has shifted 0.00025 to the right from 0
and i believe the f = 1000hz
looking at the phase shift calculator 30 degrees looks right to me ?

#### MrAl

Joined Jun 17, 2014
10,906
i think the sin has shifted 0.00025 to the right from 0
and i believe the f = 1000hz
looking at the phase shift calculator 30 degrees looks right to me ?
Hi,

If you want to make the measurement using time then you have to correlate time to phase.
You should be able to answer this question first:
What is the time for the full 360 degree phase of the sine wave? That is, how much time does it take to traverse through the entire 360 degrees.

After you do that it becomes a simple ratio.

#### WBahn

Joined Mar 31, 2012
29,507
i think the sin has shifted 0.00025 to the right from 0
and i believe the f = 1000hz
looking at the phase shift calculator 30 degrees looks right to me ?
Why does 30° look right?

If the phase angle were 30°, would you expect the min, the max, or a zero crossing to occur at t = 0?

Look at the waveform. What is happening at t = 0?

Does 30° make sense with the numbers you have above?

If f = 1000 Hz, what is the period?

What fraction of a period is the 0.00025 s (time is a dimensioned quantity -- you need to provide units)?

What fraction of a period is 30°?

Speaking of units, what are the units on Ip? 10 what? 10 mA, 10 A, 10 µA. Makes a huge difference.

#### leejohnson222

Joined Jan 11, 2023
57
Hi,

If you want to make the measurement using time then you have to correlate time to phase.
You should be able to answer this question first:
What is the time for the full 360 degree phase of the sine wave? That is, how much time does it take to traverse through the entire 360 degrees.

After you do that it becomes a simple ratio.
from the graph it takes 0.001 seconds to complete a full 360 degrees
i understood to find phase angle you use - phase angle = 360 x Time delay/ wave period
so 360 x 0.00025 / 0.001 = 90 degrees

appologies on the units, so IP = 10 amps

#### MrAl

Joined Jun 17, 2014
10,906
from the graph it takes 0.001 seconds to complete a full 360 degrees
i understood to find phase angle you use - phase angle = 360 x Time delay/ wave period
so 360 x 0.00025 / 0.001 = 90 degrees

appologies on the units, so IP = 10 amps
Ok just one more thing.
See if you can reproduce the plot now using your sine function like Vpk*sin(w*t+ph). You may find you have to change something just a little.

#### leejohnson222

Joined Jan 11, 2023
57
ok let me know if this is what you mean, when i plot this in the sin starts at +10 rather than 0

#### MrAl

Joined Jun 17, 2014
10,906
ok let me know if this is what you mean, when i plot this in the sin starts at +10 rather than 0
Hi,

No the sign change

I said plot it cause that's how you find out if you got it right.

#### leejohnson222

Joined Jan 11, 2023
57
so your saying i am wrong then? it should be - Pi/2 90 degrees

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#### MrAl

Joined Jun 17, 2014
10,906
so your saying i am wrong then? it should be - Pi/2 90 degrees
Well before i answer that, do you have a way to plot a function like:
y=Vpk*sin(w*t+ph)

If you do that, when you use the right frequency and phase angle the plot will have the same phase as that which you are trying to figure out.
Also, w=2*pi*f and you can use a different Vpk if you like because you just want to compare the phase angles.

It's better you do it this way because then you'll always know how to check your results.

#### WBahn

Joined Mar 31, 2012
29,507
so your saying i am wrong then? it should be - Pi/2 90 degrees
Telling whether something is shifted to the left or to the right is something that most people find a bit tricky, so you want to be able to reason it out.

Plot the function Ip*sin(wt) with the correct amplitude and frequency and then ask whether that function needs to be shifted to the left or to the right to match it up to the curve you are given. Since you can actually go in either direction, the question is which direction allows you to match it up first (i.e., using the smallest shift amount).

Now consider an arbitrary function

y = f(t)

If I want to shift that function to the right by To, I have two choices:

z = f(t + To)
z = f(t - To)

Which one will shift it to the right?

This is easily answered by considering what we want to have happen at the origin.

If we move the curve to the right, the value that will now be at the origin used to the to the left of the origin, meaning that it was originally at a value of the function where t was negative. That means that, when t is zero, we want the value of the argument to the new function to be negative. Which of my two choices for z do that?

#### BobaMosfet

Joined Jul 1, 2009
2,102
This one is getting me in a tangle, find Ip, f and phase angle,

I = IPsin(2pi f t - phase angle)

i have Ip = 10
to find freq i need to use 1/ time of 1 full cycle
looks to me like 1 cycle is 0.001 s
so 1/0.001 is 1000hz ?

the next part is where i cant work out phase angle, i keep watching the lecture but its not clicking
Sin is a circle. And a circle has 360 degrees. Same with Cos. So, phase angle is where the voltage happens to be on the sin/cos curve at any moment in time.

#### leejohnson222

Joined Jan 11, 2023
57
@WBahn so i understand what you mean by finding out if the wav is left or right, is this the lag and lead ?
i still have not got to grips with desmos but i think i recreated the sin wav for this problem here
https://www.desmos.com/calculator/rq0h5djifa

from what i understand i can obtain the phase angle by 360 x 0.00025/ 0.001 = 90 degrees or Pi/2
if i knew how to create a slider on desmos to shift the wav left and right i could prove this have a visual representation of the sin wav.
sorry @MrAl i cant figure out how to have the freq as a slider in desmos

#### MrAl

Joined Jun 17, 2014
10,906
@WBahn so i understand what you mean by finding out if the wav is left or right, is this the lag and lead ?
i still have not got to grips with desmos but i think i recreated the sin wav for this problem here
https://www.desmos.com/calculator/rq0h5djifa

from what i understand i can obtain the phase angle by 360 x 0.00025/ 0.001 = 90 degrees or Pi/2
if i knew how to create a slider on desmos to shift the wav left and right i could prove this have a visual representation of the sin wav.
sorry @MrAl i cant figure out how to have the freq as a slider in desmos
Ok now check out the sign of the phase angle.

I guess since you havent done this before i should point out that sometimes the sign of the phase is important and sometimes it's not. Notice you had to make the phase negative to get the plot right. If you didnt do that, you would have got a different wave because it would be shifted to the right instead of to the left. If you also drew a sine wave with no phase shift, you would see the zero crossing of the wave you plotted as being shifted to the right. That means that wave comes after the zero phase shift wave in time, so it is delayed in time, so you needed the sign this time.
In some cases it is ok to just say the phase shift is 90 degrees whether it is shifted to the left or to the right, but when you want to plot it right, you have to get the sign of the phase correct.

So with all that in mind, can you quote the signed phase shift now? We know the unsigned phase shift is 90 degrees, you got that perfect.

Also, in that desmos thing try using the variable 'x' in place of 't', or else see if you can get 't' to be the horizontal axis. As it stands i think 'x' is the horizontal so if you use 'x'
rather than 't' you should get better results and be able to set 'f' to what you want.

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#### leejohnson222

Joined Jan 11, 2023
57
thank you to everyone who replied here, i got lots of information and clarification. To be honest people made it easier to follow and understand than my online tutor who only replies after 7-10 days which is why i use this forum.

#### MrAl

Joined Jun 17, 2014
10,906
thank you to everyone who replied here, i got lots of information and clarification. To be honest people made it easier to follow and understand than my online tutor who only replies after 7-10 days which is why i use this forum.
Hi,

Yes i am amazed at how often i hear that. Maybe they are overworked with too many students.