- #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
VR1 = VC1VR1 + VRc - VC2 = 0
VR2 = VC2
IR1 + IC1 + VRC = Iinj
IRc = IR2 + VC2
[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]