Can someone please help me find expressions for i2, i3 and i5?
I know i1 must be Vin-Vx/R1.
i3 is theoretically Vx-Vout/R2, but im stuck at i5 and i2.
Thank you very much.

 

I5 = Vout/Xc1
I2=(Vx-Vout)/Xc2
Its upto you how do you define Xc. You can define it using S (laplace) or using complex variables.

 

You have I1 and I3, right? What the relationship between I1, I2, and I3?

 

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Can someone please help me find expressions for i2, i3 and i5?
I know i1 must be Vin-Vx/R1.
i3 is theoretically Vx-Vout/R2, but im stuck at i5 and i2.
Thank you very much.

Hi,

As others have pointed out, the only difference between a resistor and capacitor in calculating the current is the capacitor has a complex impedance while the resistor has just a real impedance which is called the resistance. This means we have to use complex numbers to calculate the current.

For the resistor we have:
i=v/R

and for the cap we have:
i=v/Z

where Z is the complex impedance:
Z=1/(j*w*C)

and j is the imaginary operator and w is the angular frequency equal to 2*pi*f with f the frequency in Hertz.

This is sometimes shortened to:
Z=1/(s*C)

where s=j*w.

So if we assume you know the voltage across the cap is v then we have:
i=v/z=v/(1/(s*C))

and using algebra:
i=v*s*C/1=v*s*C

and since s=j*w we end up with:
i=v*j*w*C.

This is purely imaginary which means the current is 90 degrees out of phase with the voltage.

You have to be a little careful though because here we use the impedance not the reactance. Impedance is usually represented with a Z while reactance is usually represented with an X. If we try to use reactance instead of impedance we end up with a real quantity and that is not entirely correct.