fluidistic
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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?