this is the standard integrator circuit, can someone check if my understanding is correct please

if we assume the the C = 1 mF
the resistor is Rin = 10 kOhms
the op amp will not saturate
ideal op amp
and input voltage is 10 V
trying to figure out voltage out as a function of time

the Vout is supposed to be -1/RC integral(Vin dt)


Vout = -10/(10000 * 10^-3) integral(dt) = -10/(1) = -1t

would this be correct?

so Vout = -10t ?

 

Since the opamp forces V(inv) to be 0V, the current in the 10K resistor is 1mA (10V/10K). The charge accumulated by the capacitor Q=C(ΔV) = it.
Rearrange, ΔV = it/C = (1e-3)t/1000e-6 = (1e-3)t/1e-3) = t, or 1V/1s. However, the current flow causes the output of the opamp to go negative...

 

thanks it seems as though your plot has confirmed my answer, by the way what program is it that you used to analyze this circuit

 

LTSpice. Free download at Linear.com

 

nice, thanks alot