- #26

SGT

ng said:V=Acos(wt+phi)=Acoswt+Bsinwt

L d^2i/dt +Rdi/dt +i/C=dV/dt

i=A1exp(s1t)+A2exp(s2t)

di/dt=s1A1exp(s1t)+s2A2exp(s2t)

d^2i/dt^2= s1^2A1exp(s1t)+s2^2A2exp(s2t)

i(0)=V/R

if its dc dV/dt=0

ac then dV/dt=-Awsinwt+wBcoswt

is this going wrong?

It's wrong!

i(0) is the current in the inductor prior to the application of the excitation.

[tex]\frac{di}{dt}(0)[/tex] is the derivative of the current in the inductor prior to the application of the excitation.

Since [tex]v_L(t) = L\frac{di}{dt}[/tex], we can say that

[tex]\frac{di}{dt}(0) = \frac{v_L(0)}{L}[/tex]