Hey guys
I'm just wondering if i'm on the right track for the problem. I have started analysing the circuit, but I'm really unsure of my method of analysis.
The circuit switches from position "a" to position "b" at t=0
and I'm trying to fined i(t) for t>0
from what I understand, I need to determine i(o), which is for the circuit at t=0 (containing an inductor and 4A supply).
Then determine the α and wo for the circuit at t>0
where α = 1/2RC and wo = √(1/LC).
which will indicate the formula to use for the step response, to allow for determining i(t).
my calculated values so far-
by KCL
i(0) = 4A(6/2+8)
= 3A
at t>0
I used source transformation for the 4A supply (24V)
then added the total voltage in the loop (= +12V)
α = 1/(2 x 20Ω x 0.02F)
= 1.25
wo = √(1/ (2 x 0.02))
=5
therefor I understand I need to use
v(t) = (A1cos(wd)t + A2sin(wd)t)e^(-αt)
wd = √((wo^2) - (α^2))
= √(375/16)
... which isnt a very nice looking number
have I made a mistake somewhere? Is my whole understanding of the method in answering this question just plane wrong?
Thanks guys
ps. I'm really new to the whole posting on forums (this is the first forum I have ever used). So if I do anything the is annoying or if i'm doing anything i'm not supposed to be doing, plz tell me to I can correct myself.
I'm just wondering if i'm on the right track for the problem. I have started analysing the circuit, but I'm really unsure of my method of analysis.
The circuit switches from position "a" to position "b" at t=0
and I'm trying to fined i(t) for t>0
from what I understand, I need to determine i(o), which is for the circuit at t=0 (containing an inductor and 4A supply).
Then determine the α and wo for the circuit at t>0
where α = 1/2RC and wo = √(1/LC).
which will indicate the formula to use for the step response, to allow for determining i(t).
my calculated values so far-
by KCL
i(0) = 4A(6/2+8)
= 3A
at t>0
I used source transformation for the 4A supply (24V)
then added the total voltage in the loop (= +12V)
α = 1/(2 x 20Ω x 0.02F)
= 1.25
wo = √(1/ (2 x 0.02))
=5
therefor I understand I need to use
v(t) = (A1cos(wd)t + A2sin(wd)t)e^(-αt)
wd = √((wo^2) - (α^2))
= √(375/16)
... which isnt a very nice looking number
have I made a mistake somewhere? Is my whole understanding of the method in answering this question just plane wrong?
Thanks guys
ps. I'm really new to the whole posting on forums (this is the first forum I have ever used). So if I do anything the is annoying or if i'm doing anything i'm not supposed to be doing, plz tell me to I can correct myself.