Find the charge q(t) on the capacitor and the current i(t) in the given lrc-series circuit. l = 5 6 h, r = 10 ω, c = 1 60 f, e(t) = 1200 v, q(0) = 0 c, i(0) = 0 a q(t) = correct: your answer is correct. c i(t) = correct: your answer is correct. a find the maximum charge on the capacitor. (round your answer to three decimal places.)

Explanation:

The DE corresponding to LRC series circuit is

Lq" + Rq' +1/c q = E

q" + 12q' + 72 q =  1440

considering only homegeneous part

q" + 12q'+ 72 q= 0

the auxillary equation is

the solutiion is

solve for particular siolution

q" + 12q'+ 72 q= 0

let qp = a be the solution

0 + ) + 72a = 1440

a = 20

general solution is

q = qh + qp

[/tex]

applying initial value i(0) = q(0) = 0

also i(t) = q'(t)

q(0) = 0

i(0) = 0

coil wire, increase current, put iron inside the coil