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Time Response of Reactive Circuits - Engineering

Q1:

An integrator consists of a 3.3 k resistor and a 2 F capacitor. A single 30 V, 6 ms pulse is applied to the input. How much will the capacitor charge?

A 10.3 V

B 30 V

C 12.09 V

D 17.91 V

ANS:D - 17.91 V

R=3.3 * 10^3 Ohms
C=2 * 10^-6 F
T= 6 * 10^-3 =0.006 sec
t = RC
=3.3 * 10^3 * 2 * 10^-6
= 0.0066 sec.

Then,
Change = (Final-start) * (1-1/e^T/t).
= (30 - 0) * (1-1/e^0.006/0.0066).
= (30) * (1-1/e^0.9090).
= 30 * 0.5970.
= 17.91.