12.10 Exercises 367
(i)Use Kirchhoff ’s voltage law (Section 11.7) to show that the currentI(t) in the circuit
is given by the inhomogeneous equation
(ii)Find the solution of the homogeneous equation (fordE 2 dt 1 = 10 ), and confirm that it
decays exponentially ast 1 → 1 ∞.
(iii)Show that the particular integral for the periodic e.m.f.E(t) 1 = 1 E
0
sin 1 ωtis
I
p(t) 1 = 1 I
0
1 sin(ωt 1 − 1 δ)
where andSL.
C
=−ω
ω
1
I
E
RS
S
R
0
0
22
=
,= tanδ ,
L
dI
dt
R
dI
dt
I
C
dE
dt
2
2
++=