The maximum charge on the capacitor is : 0.0317 C
Given data :
L = 1 H
R = 100 Ω
C = 0.0004 f
E(t) = 20 V, q(0) = 0 C,
i(o) = 3A,
Determine q(t) and i(t)
we will apply the Kirchhoff's second law to the system
Lq'' + Rq' + [tex]\frac{1}{c} q =[/tex] E(t)
= q'' + 100q' + 2500q = 20 ---- ( 1 )
The auxiliary equation is expressed as
r² + 100r + 2500 = 0
∴ r = -50,-50
y₁ = e⁻⁵⁰[tex]^{t}[/tex] , y₂ = e[tex]^{-50t}[/tex]
q = a
back to equation ( 1 )
0 + 100(0) + 2500(q) = 20
∴ a = [tex]\frac{1}{125}[/tex]
