(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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) = A_{2}te^{-20t}

Where i need to find what is the cosntant A_{2}

2. Relevant equations

R = 100Ohm

L = 2.5H

C = 1mF

i(0) = 0A

v_{C}(0) = 24V

v_{L}= L di/dt

v_{R}= iR

di/dt = -20A_{2}te^{-20t}

3. The attempt at a solution

I apply KVL to the closed RCL loop and get:

v_{C}+ v_{L}+ v_{R}= 0

v_{C}(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 -20A_{2}te^{-20t}so

di(0)/dt = -9.4 = -20A_{2}(0)e^{-20(0)}

-9.4 = 0

which is fallacy

but according to the book:

A_{2}= -9.4

so,

i(t) = -9.4te^{-20t}

Where did i go wrong?

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# Help with Second Order Circuits

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