Finding Vo(t) After 125ms in Ideal Circuit w/ Charged Capacitor

[Studious_stud]

Homework Statement

If the op amp in the following circuit is ideal and operating in the linear region, and the capacitor is initially charged to 2V, find the output voltage Vo(t) after 125ms

Homework Equations

Voltage divisor rule, converting to impedance

The Attempt at a Solution

Transform into phasor domain, convert back into time domain?

I really have no idea how to go about this one, the fact that the capacitor is charged and finding the output voltage after 125ms is throwing me off.

I'm quite weak at circuits anyway, but unfortunately I have to take one module in them...

Thanks for any help guys, would be great.

 

[Redbelly98]

Since it's a DC input, it may be easiest to use the relation between current and voltage for a capacitor here.

 

[stevenb]

Transform into phasor domain, convert back into time domain?

I really have no idea how to go about this one, the fact that the capacitor is charged and finding the output voltage after 125ms is throwing me off.

I'm quite weak at circuits anyway, ...

This is a problem where a strength in math will make up for a weakness in circuits. This circuit is an ideal integrator (with the assumptions given). You could solve this one with phasors or in the frequency domain, but I would suggest staying in the time domain on this one.

You can use the capacitor relation i=C dv/dt, Ohms law i=v/R and the fact that the negative terminal of the opamp is a virtual ground (i.e. it is held at ground potential even though not connected to ground) to derive an output voltage which is an integral of the input voltage. The initial charge on the capacitor will be related to the integration constant to fix the initial conditions.

So here you are just integrating the constant input signal and you know that the integral of a constant is a linear ramp.

Post your attempt at this and we can guide you if you have trouble.