# Solving Phasor Circuit: Finding Theta

• EvLer
In summary, the conversation is about a problem involving a series circuit with an independent current source, resistor, and inductor. The voltage across the inductor is given as 3cos(wt + theta) and the goal is to find theta. By using the impedance for the inductor, the speaker was able to determine the voltage as jwL5 /_ 0 which is also equal to 3/_theta. The answer for theta is 90 degrees, which can be found by using the arctan of Im[Z]/Re[Z]. The speaker also mentions the textbook DeCarlo and Lin as a good resource for intro EE courses.
EvLer
Hello,
now we are in phasors and I am missing something in this problem:
given a circuit of indep current source (5cos(wt)), R, L (with vL(t)) all in series, no values for them,
although voltage across inductor vL(t) = 3cos(wt + theta), we need to find theta.

So, by using impedance for L: Z = jwL, vL(t) = Z*I,
so I got vL(t) = jwL5 /_ 0 which is also = 3/_theta
And now what? The answer is 90 degrees, but how do I get it?

Thanks a lot.

Last edited:
The reason its 90 degrees is simple... the voltage is indeed ZI, and I has a phase of zero--- but you would do well to convince yourself that the impedance Z is purely imaginary, so you have a phase for your impedance equivalent to the arctan of Im[Z]/Re[Z] where Re[Z] = 0, and thus you have an arctan of infinity, which is undoubtedly equal to 90 degrees.

Therefore you have V = ZI which yields a phase of 0 + 90, the angular frequency and the amplitudes of Z and I are immaterial for this problem.

By the by, do you intro EE students still happen to make use of Nilsson and Riedel by any chance?

Theelectricchild said:
By the by, do you intro EE students still happen to make use of Nilsson and Riedel by any chance?
Huh?
I guess, not.

Oh sorry, it's just a textbook that I found really great for my intro EE courses.

Theelectricchild said:
Oh sorry, it's just a textbook that I found really great for my intro EE courses.
Thanks, I might check it out as complementary source. We are using DeCarlo and Lin, since DeCarlo is actually a professor here, I doubt they will change our texbook any time soon

## 1. What is a phasor circuit?

A phasor circuit is an electrical circuit that uses phasors, which are complex numbers, to represent the amplitude and phase of a sinusoidal voltage or current. This allows for easier analysis and calculations in AC circuits.

## 2. How do I solve a phasor circuit?

To solve a phasor circuit, you will need to use complex numbers, Ohm's law, and Kirchhoff's laws. First, convert all voltage and current values to their phasor form. Then, use Kirchhoff's laws to set up equations and solve for unknown phasors. Finally, convert back to the time domain to get the solution.

## 3. What is theta in a phasor circuit?

Theta, denoted as θ, represents the phase angle in a phasor circuit. It is the angular displacement between the voltage and current waveforms, and it is measured in degrees or radians.

## 4. How do I find theta in a phasor circuit?

To find theta in a phasor circuit, you can use the inverse tangent function (tan-1) to calculate the ratio of the imaginary and real parts of the phasors. This will give you the angle in radians, which can then be converted to degrees if needed.

## 5. Can I use phasor analysis for all types of circuits?

No, phasor analysis is only applicable to AC circuits with sinusoidal sources. It cannot be used for DC circuits or circuits with non-sinusoidal sources.

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