- #1

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 [tex]V_{AB}=V_B-V_A[/tex] then [tex]|V_{AB}|^2=V_0^2[/tex] for all [tex]\omega[/tex].

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 [tex]\omega[/tex] is the angular frequency and [tex]V_0[/tex] is the amplitude of [tex]V(t)[/tex].

What I did so far : I notice that the current through both loops is the same and is worth [tex]I=\frac{V(t)}{Z}[/tex] where [tex]Z=R-\frac{i}{\omega C} \Rightarrow I(t)=\frac{2V_0 \cos (\omega t + \phi)\cdot \omega C}{\omega C R-i}[/tex].

How is that possible that the current is has an imaginary part? I guess I made an error, could you confirm?