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I got this question wrong, but I am not sure why it is wrong. The only part of the question I got right was the time constant, which is 8 seconds. I have attached the question as an image. The question asks for the constants A1 and A2.

Problem Circuit

This question was from self-paced online test, with no college credit. That being the case, you cannot see the correct answer afterwards, nor can you see what the thought process is to determine the solution. You simply are told right or wrong. So I'm looking for how to approach determining what A1 and A1 need to be. Here is what I was thinking:

In saturation, the MOSFET equation that is being used is IDS = K/2*(VGS-VT)**2, with K as described in the problem. It's assumed that no current can enter the gate of the MOSFET.

So based on that, with VGS = 5V (up until time T), and VT = 3V, the MOSFET operates in saturation up to time T. In saturation, I tried to model the circuit as I thought it would look like: Modeled Circuit

Initially, at time 0, I thought the capacitor would act as an open circuit, no current would flow through it, so the resistor carried all the current, and that meant initial the output voltage would be 10V (which I know is wrong, but I don't know why).

I then thought the voltage across the capacitor after t=0, but t < T, would be: v=10*(1-exp(-t/8)), the 8 being the time constant based on the the resistance and capacitance, I used the rising exponential form because the initial condition states no charge is on the capacitor at t=0. I had thought about taking the derivative of the voltage across the capacitor using C * dv/dt + VDD/R = 0.05, but that doesn't help anything.

I am not sure how to proceed to determine A1 and A2, also, if my modeled circuit is not correct, please let me know what I did wrong.

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