What is the current through the emf in a circuit with capacitors and resistors?

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The discussion revolves around solving a problem involving a circuit with capacitors and resistors from Purcell's Electricity and Magnetism. The main focus is on finding the current through the emf, demonstrating a relationship between voltages, and determining the phase difference between current and voltage in the circuit. The user expresses confusion regarding the presence of an imaginary part in the current calculation, which is clarified as a common aspect of phasor notation in AC circuits. The conversation emphasizes the importance of understanding complex numbers in electrical engineering. Overall, the thread highlights key concepts in analyzing AC circuits with capacitors and resistors.
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Homework Statement


I'm trying to solve the problem 8.12 in Purcell's book on Electricity and Magnetism.

The circuit is like that :

|--------------|------------|
|......|.....R
|......C...|
emf...|...C
|......R...|
|--------------|-------------
(The points represent nothing, I had to write them because otherwise the circuit wouldn't appear as I'd like).
1)Find the current passing through the emf.
2)Demonstrate that if V_{AB}=V_B-V_A then |V_{AB}|^2=V_0^2 for all \omega.
3)Find the phase difference between the current that passes through the emf and a capacitor.

Homework Equations


None given.

The Attempt at a Solution


I'm currently trying to do part 1).
I forgot to mention that \omega is the angular frequency and V_0 is the amplitude of V(t).
What I did so far : I notice that the current through both loops is the same and is worth I=\frac{V(t)}{Z} where Z=R-\frac{i}{\omega C} \Rightarrow I(t)=\frac{2V_0 \cos (\omega t + \phi)\cdot \omega C}{\omega C R-i}.
How is that possible that the current is has an imaginary part? I guess I made an error, could you confirm?
 
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fluidistic said:
How is that possible that the current is has an imaginary part? I guess I made an error, could you confirm?

currents and voltages both can have an "imaginary part" (I hate the name "imaginary", so misleading).

It's usually written in phasor notation, so you'd convert the cartesian form:

x + iy
to the polar form
r^{i\theta}

and then write it in phasor notation:
r \angle \theta
 
Pythagorean said:
currents and voltages both can have an "imaginary part" (I hate the name "imaginary", so misleading).

It's usually written in phasor notation, so you'd convert the cartesian form:

x + iy
to the polar form
r^{i\theta}

and then write it in phasor notation:
r \angle \theta
Ok thank you, I understand.
Is my answer correct though?
 
fluidistic said:
Ok thank you, I understand.
Is my answer correct though?

that I can't say for sure, but I can tell you that it's what I would have done.
 
Pythagorean said:
that I can't say for sure, but I can tell you that it's what I would have done.
Thank you once again. :smile:
 
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