An RC circuit has an AC supply given (in volts) by 400 cos 2t, a resistance of 100 ohms, and a capacitance of 10-2 farad. Initially there is no charge on the capacitor. Find the current in the circuit at any time t.
Answers
Answered by
0
Answer:
5
1
(23e
−4t
+sin(2t)+2cos(2t))
The circuit equation is E=
dt
dq
R+
C
q
Where R is the resistance,C is the capacitance,E is the EMF supply and q is the charge,
Substituting the given values gives,
300cos(2t)=150
dt
dq
+
600
q
⟹2cos(2t)=
dt
dq
+
90000
q
This is a Linear Differential equation in q,
The integrating factor is e
90000
t
⟹qe
90000
t
+c=∫2e
90000
t
cos(2t)dt
Given that Intital charge of th capacitor is 5coulombs,
Which gives the value of integration constant c,
∴ charge on the capacitor at time t is
5
1
(23e
−4t
+sin(2t)+2cos(2t))
Similar questions