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cshum00
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Homework Statement
I have a RLC circuit in series. I am trying to find the current i(t) passing through this RCL circuit. When solving the RCL circuit, it happened to be critically damped. And simplified i ended up with:
i(t) = A2te-20t
Where i need to find what is the cosntant A2
Homework Equations
R = 100Ohm
L = 2.5H
C = 1mF
i(0) = 0A
vC(0) = 24V
vL = L di/dt
vR = iR
di/dt = -20A2te-20t
The Attempt at a Solution
I apply KVL to the closed RCL loop and get:
vC + vL + vR = 0
vC(0) + L di(0)/dt + i(0)R = 0
24V + 2.5H di(0)/dt + 0 = 0
di(0)/dt = -24V/2.5H = -9.4A
But di/dt is also -20A2te-20t so
di(0)/dt = -9.4 = -20A2(0)e-20(0)
-9.4 = 0
which is fallacy
but according to the book:
A2 = -9.4
so,
i(t) = -9.4te-20t
Where did i go wrong?