# Find the phase angle of the RLC source

#### Luiz Fernando Vieira

Joined Aug 24, 2015
66
Hello, I am having difficulty solving this problem using a parallel RLC circuit to find the voltage phase, I stopped here and would like some help to continue.

MOD NOTE: The TS provided clarifying information below that the source voltage is 20cos(2t) V (i.e., frequency is 2 rad/s).

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#### MrAl

Joined Jun 17, 2014
11,280
Hello, I am having difficulty solving this problem using a parallel RLC circuit to find the voltage phase, I stopped here and would like some help to continue.
Voltage phase is whatever the voltage source assumes because it is a parallel RLC circuit.
Did you mean some current phase?

Also, what is the frequency? It's not 1/pi is it, but maybe it is?

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#### WBahn

Joined Mar 31, 2012
29,885
What is the frequency of your source? Your work implies that it is 2 rad/s. Where is that coming from?

How many farads is 2 nF? How many farads is 2 µF? Look carefully at what you are using.

It's never a good idea to force the reader to back out basic given information from your work -- but at least you are showing your work, so big kudos for that.

After you calculate the impedance of each of the three components, you are just adding them together. Impedances in series add. How do impedances in parallel combine?

#### Luiz Fernando Vieira

Joined Aug 24, 2015
66
sorry, I cut it in the image where the value is ....20 cos(2t)

#### MrAl

Joined Jun 17, 2014
11,280
sorry, I cut it in the image where the value is ....20 cos(2t)
Hello again,

Oh ok, no problem, but how about posting the entire drawing now?
You could also post the frequency in Hertz or in rads/sec. We can assume from your work what it is but it is better that you mention it so we can verify you did the problem right.

There are a lot of members here who would be happy to help you but you do have to post the entire problem and possibly some parameters you used in your work.

For another example of the guesswork, maybe you are looking to find the phase of the current through the network?
If that is true, then it looks like you did something right, almost.
It looks like you added the admittances which is right, but you did not consider all the possible phase angles using atan(x) and then select the correct one.
You have to figure out how to use atan(x) correctly, or use atan2(imag,real) and go from there.
The right result for the phase of atan(x) depends on the signs of the numerator and denominator of x:
x=n/d
Go over that one more time see what you can come up with.

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#### Luiz Fernando Vieira

Joined Aug 24, 2015
66
Hello again,

Oh ok, no problem, but how about posting the entire drawing now?
You could also post the frequency in Hertz or in rads/sec. We can assume from your work what it is but it is better that you mention it so we can verify you did the problem right.

There are a lot of members here who would be happy to help you but you do have to post the entire problem and possibly some parameters you used in your work.

For another example of the guesswork, maybe you are looking to find the phase of the current through the network?
If that is true, then it looks like you did something right, almost.
It looks like you added the admittances which is right, but you did not consider all the possible phase angles using atan(x) and then select the correct one.
You have to figure out how to use atan(x) correctly, or use atan2(imag,real) and go from there.
The right result for the phase of atan(x) depends on the signs of the numerator and denominator of x:
x=n/d
Go over that one more time see what you can come up with.

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#### MrAl

Joined Jun 17, 2014
11,280
Hello again,

What you have to do is go over your atan(x) calculation and observe the sign of the numerator of x and the denominator of x so you can decide what quadrant the phase shift is in. You can do it relative to a sine wave because you seek the steady state AC solution, but you may have to compensate because it is a cosine excitation wave.
Do you understand these two points?

When it comes to calculating phase shifts in electrical circuits, atan(x) is ambiguous to the extent that it may not be able to get the correct quadrant for the phase shift. You have to do that yourself when you use atan(x), which means you may have to alter the quadrant manually after calculating atan(x) numerically. The quadrant comes from the sign of the numerator and denominator of x as x is expressed with the imaginary part on top and the real part on the bottom:
x=imag/real
The imag part is considered to be on the vertical axis while the real part is on the horizontal axis.
If the imag part is positive the phase shift lies above the horizontal axis, and if the imag part is negative is lies below the horizontal axis, and also if the real part is positive then the phase shift lies somewhere to the right of the vertical axis, and if the real part is negative then the phase shift lies somewhere to the left of the vertical axis.
Taking both the imag part and real parts into account like this, we can zero in on the quadrant.
Now in computing atan(a) we have some examples (I am using 'a' here as parameter instead of 'x' or 'y')...
For example:
a=2/4
The imag part is positive so the phase angle is above the horizontal axis, and the real part is positive so it is somewhere to the right of the vertical axis. The combination of these facts tells us the angle is in the first quadrant.
For other examples:
a=-2/4
The imag part is negative and the real part is positive, so the angle lies in the fourth quadrant.
a=-2/-4
The imag part is negative and the real part is negative, so the angle lies in the third quadrant.

Here is a little diagram that summarizes the determination of the quadrant.
The first sign shown represents the imaginary part, the second sign shown represents the real part, so the signs:
- +
indicate the imag part is negative and the real part is positive. that puts it in the fourth quadrant.
Angles in the third and fourth quadrants are considered negative.

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#### MrAl

Joined Jun 17, 2014
11,280
Hello, I am having difficulty solving this problem using a parallel RLC circuit to find the voltage phase, I stopped here and would like some help to continue.

MOD NOTE: The TS provided clarifying information below that the source voltage is 20cos(2t) V (i.e., frequency is 2 rad/s).
Hello again,

Taking another look at your work, it appears you may have calculated the phase of the impedance not the current.
You have to create the expression for the current, then find the phase of that.

If the impedance is Z and the source voltage is E, then the current is:
I=E/Z
and that puts Z in the denominator and so the phase of the current is different than just the phase of Z. This could make a very big difference.

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