Question

Suppose that L = 2, R = 40, E(t) = 100e^-10t, and I(0) = 0. Find the maximum current in the circuit for t >= 0.

Answer 1

is it parallel or series ?

Answer 2

I don't think that information is relevant here.

Answer 3

Ldi/dt+Ri=E(t)
2di/dt+40i=100e-10t
di/dt+20i=50e-10t
i(t)=ce-20t+5e-10t
i(0)=0=c+5->c=-5
i(t)=-5e-20t+5e-10t
di/dt=0-> 100e-20t=50e-10t
e-10t=1/2-> e-20t=1/4
imax=-5/4+5/2=5/4

Answer 4

Wait. I(t) = ce^-20t + 5e^-10t. Where does that come about?

Answer 5

y'+ay=b(t)
y=ce-at+e-at(int e^at*b(t))

Answer 6

Suppose a is a constant.

Answer 7

Wouldn't the particular solution Ip = Ke^-10t

Answer 8

yes for particular form you can choose k and then find it out.