- #1

no_alone

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## Homework Statement

Hi, I already asked a question close to this, but now I have different conditions.

This is the circuit

[itex] C_1 = C_2 \\

R_1= R_2[/itex]

The current is an AC , and I would like to know the voltage at R_1 and at R_2

I made some progress but I do not really know hot to continue.

## The Attempt at a Solution

V

_{R1}= V

_{C1}

V

_{R1}+ V

_{Rc}- V

_{C2}= 0

V

_{R2}= V

_{C2}

I

_{R1}+ I

_{C1}+ V

_{RC}= I

_{inj}

I

_{Rc}= I

_{R2}+ V

_{C2}

[tex] V_1 = V_{C1} = V_{R1} \\ V_2 = V_{R2} = V_{C2} [/tex]

[tex] \frac{V_1}{R_1} + \frac{dV_1}{dt}*C_1 + \frac{V_{Rc}}{R_c} = I_{inj} \\

\frac{V_{Rc}}{R_c} = \frac{V_2}{R_2} + C_2*\frac{dV_2}{dt}\\

[/tex]

[tex] \frac{dV_1}{dt}*C_1 = I_{\omega} -\frac{V_1-V_2}{R_c} - \frac{V_1}{R_1} \\

\frac{dV_2}{dt}*C_2 = -\frac{V_2}{R_2} +\frac{V_1-V_2}{R_c} \\

--> C_1 == C_2 , R_1 == R_2 \\

\frac{dV_1}{dt} = \frac{I_{\omega}}{C_1} -\frac{V_1-V_2}{R_c*C_1} - \frac{V_1}{R_1*C_1} \\

\frac{dV_2}{dt} = -\frac{V_2}{R_1*C_1} +\frac{V_1-V_2}{R_c*C_1} \\

[/tex]