Question

A voltage pulse of amplitude 10V begins at 5 sec and lasts for 20 msec,which is short compared with the response times and time constants of the system.This impulse is then passed through an integrator.Determine an expression for the output voltage e(t) of the intergrator.
1) 0.2 u(t-5)
2) 0.2 u
3) 5t^2 u(t)
4) 50 u(t-0.02)

Answer 1

The first one (0.2 u(t-5)) is correct. Integrator will integrate the incoming pulse, and therefore:
* Nothing happens (the output is zero) before 5 sec.
* After that, the output will rise for 20 milliseconds at constant speed.
* The total integral is 0.02 seconds times 10 volts, which is 0.2.