Q. Draw and explain an RC integrator .Derive the relation between input  and output voltage.

Solution:

A circuit in which the output voltage is directly proportional  to the integral of the input  is known as an integrator circuit i.e,

Output ∝ input

An integrator circuit is a simple RC series circuit with output taken across the capacitor  as shown in figure

let ei be the input alternating voltage let i be resulting alternating current . Since R is very large as compared to capacitive reactance Xc of the capacitor,it is reasonable to assume that voltage across R(i.e. eR) is equal to the input voltage i.e,

                             e_i =eR

                              i = eR /R