Find current for circuit with capacitor, resistor, capacitor in series

[Cyrus]

I have to solve this problem for a circuit. Its a capacitor, a resistor and another capacitor all in series.

Both capacitances are the same, 1uF, and the resistor is 100k-Ohm.

I have to find the current function of time.

What I did was use KVL to get:


$$- \frac{1}{c_1} \int i(t)dt + v_1 (t_0) + \frac{1}{c_2} \int i(t)dt + v_2 (t_0) + R i(t) = 0$$

Then I took the derivative to get:

$$- \frac{1}{c_1} i(t) + R \frac {di}{dt} + \frac{1}{c_2}i(t) =0$$

Which simplifies to:

$$R( \frac{1}{c_2} - \frac {1}{c_1} )^{-1} \frac {di}{dt} +i(t) = 0$$

But the two capacitances have the same value, which means that RC-eq is zero. That's wrong...hmmmmmmmmm

 

[barob1n]

WTF. Why not change the signs of one of the capacitances. They should have the same sign. Or just let the combined capacitance equal to .5uF.

 

[Cyrus]

Because based on the diagram, they are in the passive configuration which is why it is negative.