Solving this electronic problem with impedance ?

enter image source here

There is two of this image in series, two capacitors C1 C2 and two resistors R1R2

To be more precise this is two real capacitors (capacitor and resistor in parallel) in series.

So i have the differential equation etablished by Kirchhoff's laws :

i(1R1+1R2)+(C1+C2)didt=C1C2d2udt2+(C2R1+C1R2)dudt+uR1R2

i tried to do it by impedance because i thought it will take less time.

Impedance of the first real capacitor :

Z1=(1ZC1+1ZR1)1=ZR11+ZR1ZC1

Impedance of the second :

Z2=(1ZC2+1ZR2)1=ZR21+ZR2ZC2

the equivalent impedance of the entire circuit is :

Zeq=Z1+Z2

and then Zeq=ui

but it lead to

i=1R1(u+R1C1jwu)+1R2(u+R2C2jwu)

and :

i=u(1R1+1R2)+dudt(C1+C2)

j is the imaginary unit

Obviously it's not the same, i know i'm good with Kirchkoff's law because i checked the answer, but i'm not good with impedance, why ?

1 Answer
Mar 29, 2018

See below.

Explanation:

When you solve using impedances you are assuming that the circuit is submitted to a sinusoid periodic input. You are solving without considering the transient modes. So be careful with this approach.