Question

for a op amp based integrator with C = 1 uF, R =1M, Vin = .1v, what is the time dependence of the output voltage?

Answer 1

The op amp based integrator circuit is shown below

Since the potential difference between points a and b is nearly zero therefore a will act like virtual ground. We can obtain relationship between input and output voltage by applying Kirchoff's law at point a.

If we integrate both sides of equation (1) then it will give us expression for time dependent output voltage.

If we put the given values of R and C in equation (2) i.e. the expression of output voltage then we will get the time dependence of output voltage in this case.

Equation (3) gives the time dependence of output voltage.