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i_am_stupid
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Homework Statement
For the below circuit, the switch was open for a long time. Find the current Ia(t) for t>0. All capacitors are initially uncharged.
Homework Equations
Complete response of a capacitor: v(t) = Voc + (v(0) - Voc)e^(-t/τ)
Combining parallel capacitors: summation
Current through a capacitor: i = Cdv/dt
The Attempt at a Solution
I began by combining the three capacitors on the right side into a single 500μF capacitor connected in series with the 3K resistor.
Because the switch was open for a long time, we can assume the circuit has reached steady state, at which point the capacitor behaves as an open circuit. Since no current is flowing through this branch, the 3K resistor has no voltage, and the initial capacitor (open circuit) voltage is 12V by KVL. v(0-) = v(0+)
However, opening the switch does not seem to change anything, because after the circuit has once again reached steady state the capacitor acts like an open circuit once again, with a voltage of 12V by the same reasoning as before.
So, my equation would work out to be v(t) = 12 + (12 - 12)e^(-t/τ) = 12. Is this correct, or am I missing something?
Also, the question asks for the current through the 3K resistor, so would this be found by [12 - v(t)] / 3K?
Thanks.