Second Order Circuit

Thread Starter

Bernardri

Joined Dec 17, 2018
5
Hello, I would like some help with this second order circuit exercise.

I did'nt understand why the solution says that V (0) = -30 V.

Also, I did not understand why the capacitor's voltage (Vc) is -30 V.

Isn't the voltage for t <0 (when the capacitor is loaded) the same as the voltage source?

The exercise asked for the circuit below i(t) for t>0 . The switch opens at t=0 after a long time closed
8.20.png

My attempt:

For t<0: V(0)= 30 V and i(0)= 15 A

For t>0:

α= R/(2L)= 2/(2*0,5)= 2

omega = 1/sqrt (LC) = 1/sqrt(0.5*0.25) = 2.82942712475

Under-damped:

di/dt= -2(15 cos(2t)+ B sin(2t))e^-2t + (-2*15 sin (2t) + 2 Bcos(2t))e^2t

di(0)/dt = -30+ 2B = -(1/L) [R*i(o)+ Vc(0)] = -2 [30+30] = -120

-30+2B=-120

B= -45

i(t)= 15 cos (2t) + (-45 sin (2t))e^-2t A

So, the answer isn't the same as the book's solution.
 

MrAl

Joined Jun 17, 2014
9,151
Hello, I would like some help with this second order circuit exercise.

I did'nt understand why the solution says that V (0) = -30 V.

Also, I did not understand why the capacitor's voltage (Vc) is -30 V.

Isn't the voltage for t <0 (when the capacitor is loaded) the same as the voltage source?

The exercise asked for the circuit below i(t) for t>0 . The switch opens at t=0 after a long time closed
View attachment 166014

My attempt:

For t<0: V(0)= 30 V and i(0)= 15 A

For t>0:

α= R/(2L)= 2/(2*0,5)= 2

omega = 1/sqrt (LC) = 1/sqrt(0.5*0.25) = 2.82942712475

Under-damped:

di/dt= -2(15 cos(2t)+ B sin(2t))e^-2t + (-2*15 sin (2t) + 2 Bcos(2t))e^2t

di(0)/dt = -30+ 2B = -(1/L) [R*i(o)+ Vc(0)] = -2 [30+30] = -120

-30+2B=-120

B= -45

i(t)= 15 cos (2t) + (-45 sin (2t))e^-2t A

So, the answer isn't the same as the book's solution.
Hello,

Are there some things missing from this problem statement?
I ask because the bottom of the second circuit diagram looks like it is missing.

Also, is the -30v the initial cap voltage? That's what it looks like, but it would be better if we could see the whole problem statement and also the solution too. This is not a difficult problem but we need the exact problem specification to answer adequately.
 
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