Phasor circuit solving for current

In summary, the conversation discusses the process of solving a linear circuit with multiple sources and the importance of considering each frequency separately. The speaker also mentions the need to convert solutions to the time domain before adding them together. They also acknowledge the cleverness of noticing the resonances and short circuits in the circuits.
  • #1
gfd43tg
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As I am trying this problem, I convert the current source to e^(j30°). I am not sure what I should do with that. I added it to the other current source that I did a source transformation on. By the way, all the components should have the same frequency as the voltage source, right? The frequency of the current source doesn't affect the impedance of the capacitors and inductors?
 

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  • #2
Here is my attempt

ImageUploadedByPhysics Forums1399361454.312838.jpg


ImageUploadedByPhysics Forums1399361474.282759.jpg
 
  • #3
It's a linear circuit, so you can determine Ix due to one source (with the other source "disabled"), and then determine Ix due to the second source (after "disabling" the first).

The circuit's Ix will be the sum of those two components, which you express by simply writing a "+" sign between the two above components because they are not of the same frequency.
 
  • #4
You need to solve for each frequency separately. Convert each solution into the time domain, then add in the time domain. You can't avoid converting to the time domain separately for w1 and w2 before the final addition.
 
  • #5
Here is my attempt, I think he had a little trick going

ImageUploadedByPhysics Forums1399689409.371969.jpg
 
  • #6
You were clever to notice the resonances of the two L-C circuits & that there is a short circuit at each frequency. And your final answer is 100% correct! Nice work.
 

1. What is a phasor circuit?

A phasor circuit is a type of circuit that uses phasors, which are complex numbers that represent the amplitude and phase of an alternating current (AC) signal. This allows for the analysis and solving of AC circuits using mathematical techniques.

2. How do you solve for current in a phasor circuit?

To solve for current in a phasor circuit, you will need to use Ohm's Law, which states that current (I) equals voltage (V) divided by resistance (R). In a phasor circuit, these values are represented by complex numbers and can be solved using vector addition and subtraction.

3. What is the difference between a phasor and a regular vector?

A phasor is a type of vector that is specific to AC circuits, whereas a regular vector can represent any type of quantity. Phasors have a magnitude and phase angle, while regular vectors have a magnitude and direction.

4. Can you solve for current in a phasor circuit without using complex numbers?

No, complex numbers are an essential part of solving for current in a phasor circuit. They allow for the representation of amplitude and phase, which are necessary for analyzing AC signals.

5. Are there any limitations to using phasor circuit analysis?

While phasor circuit analysis is a powerful tool for solving AC circuits, it does have limitations. It assumes that the circuit is in steady-state, meaning that all voltages and currents have reached their final values. It also does not take into account any transient effects or non-linear elements in the circuit.

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