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Explanation & Answer
Done dude😎 Reach me in case of needed modifications 😇
a)
Applying Kirchhoff’s voltage law on the large mesh we get
𝑒𝑖 = 𝐿
𝑑𝑖
+ 𝑒𝑐
𝑑𝑡
Rearranging the equation above
𝑑𝑖
𝑑𝑡
=
1
𝐿
𝑒𝑐
𝑖1 =
(𝑒𝑖 − 𝑒𝑐)
(1)
(Ohm’s law)
𝑅
𝑖2 = 𝑐 ∗
𝑑 𝑒𝑐
𝑑𝑡
Applying Kirchhoff’s current law on the shown node above we get
𝑖 = 𝑖1 + 𝑖2
𝑖 =
𝑒𝑐
𝑑 𝑒𝑐
+ 𝑐 ∗
𝑅
𝑑𝑡
Rearranging the equation above
𝑑 𝑒𝑐
𝑑𝑡
=
1
𝐶
(𝑖 −
𝑒𝑐
𝑅
)
(2)
State space
b) Using MATLAB, a function and a script were built using ODE45
The function
The script
The results
Done 😎
Problem CFN 6.3
Applying Kirchhoff’s current law at node 2 we get
i1 = i2 + i3
Substituting we get (1)
Applying Kirchhoff’s current law at node 3 we get
iL + iR2 = iR3
Substituting we get (2)
Applying the conditions R1 = 6 , R2 = 2 , R3 = 12, R4 = 3 , L=3 , (1) becomes (3) as follows
And (2) becomes (4) as follows
Now, we differentiate eq (4) to get (...
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