- #1

- 197

- 4

## Homework Statement

Consider a circuit consisting of a voltage source with [tex]V = V_0 \sin{\omega t}[/tex], a resistor, a capacitor, and an inductor, all connected in series. The problem is to find the steady state current as a function of omega.

## Homework Equations

[tex]V = IZ[/tex]

[tex]Z = Z_R + Z_C + Z_L[/tex]

Take

[tex]Z_R = 1 \Omega[/tex]

[tex]Z_C = -i2[/tex] Fd

[tex]Z_L = +i4[/tex] H

## The Attempt at a Solution

I find the total impedance to be

[tex]Z = 1+2i[/tex].

So I'm guessing that the maximum amplitude of the current will be [tex]V_0 \over \sqrt{5}[/tex].

Now, I'm not sure how to handle the phase. From what I remember, a resistor doesn't affect the phase, a capacitor shifts the current ahead 90 degrees compared to the voltage, and an inductor shifts it 90 degrees behind. So I would think that the total phase is zero and we get [tex]I = {V_0\over \sqrt{5}}\sin\omega t[/tex].

But then what does the angle associated with Z (i.e. \tan^{-1} 2) have to do with it.

Also, will the current have the same profile (and phase) everywhere in the circuit, or does it depend on "where" we measure the current in the circuit??

Any help would be great.