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Q&A Voltage of tank circuit is invalid

In a previous question we found that for a critically damped oscillation: $$ I(t) = 2 t e^{-0.5 t} $$But if we integrate to find the voltage through the capacitor: $$ V_{CO} + \frac{1}{C} \cd...

1 answer  ·  posted 3y ago by MissMulan‭  ·  edited 1y ago by Lorenzo Donati‭

#4: Post edited by user avatar Lorenzo Donati‭ · 2023-08-05T15:50:16Z (over 1 year ago)
Retagged.
#3: Post edited by user avatar Lorenzo Donati‭ · 2021-10-11T12:28:36Z (about 3 years ago)
Substituted formula images with MathJax syntax (with corrections). Some grammar edit.
Voltage of  tank circuit is invalid
  • In a [previous](https://electrical.codidact.com/posts/282585) question we found that for a critical damped oscillation:
  • ![Hi](https://electrical.codidact.com/uploads/YFDDpFztyswF1qeinfqvuZVj)
  • But if we integrate to find the voltage through the capacitor:
  • ![hI](https://electrical.codidact.com/uploads/Yx3t6FRnMKZTqBAPGycqk2ra)
  • the integral is always a positive value which doesnt make any sense since the capacitor is being discharged.
  • What am I doing wrong here?Help appreciated!
  • In a [previous](https://electrical.codidact.com/posts/282585) question we found that for a critically damped oscillation:
  • $$
  • I(t) = 2 t e^{-0.5 t}
  • $$
  • But if we integrate to find the voltage through the capacitor:
  • $$
  • V_{CO} + \frac{1}{C} \cdot \int_0^t{I(t)}dt
  • $$
  • the integral is always a positive value which doesn't make any sense since the capacitor is being discharged.
  • What am I doing wrong here? Help appreciated!
#2: Post edited by user avatar MissMulan‭ · 2021-07-13T12:32:07Z (over 3 years ago)
  • In a [previous](https://electrical.codidact.com/posts/282585) question we found that for a critical damped oscillation:
  • ![Hi](https://electrical.codidact.com/uploads/YFDDpFztyswF1qeinfqvuZVj)
  • But if we integrate to find the voltage through the capacitor:
  • ![Hi](https://electrical.codidact.com/uploads/ZCKF5vt61PecH38JsLeti9KW)
  • the integral is always a positive value which doesnt make any sense since the capacitor is being discharged.
  • What am I doing wrong here?Help appreciated!
  • In a [previous](https://electrical.codidact.com/posts/282585) question we found that for a critical damped oscillation:
  • ![Hi](https://electrical.codidact.com/uploads/YFDDpFztyswF1qeinfqvuZVj)
  • But if we integrate to find the voltage through the capacitor:
  • ![hI](https://electrical.codidact.com/uploads/Yx3t6FRnMKZTqBAPGycqk2ra)
  • the integral is always a positive value which doesnt make any sense since the capacitor is being discharged.
  • What am I doing wrong here?Help appreciated!
#1: Initial revision by user avatar MissMulan‭ · 2021-07-13T11:45:05Z (over 3 years ago)
Voltage of  tank circuit is invalid
In a [previous](https://electrical.codidact.com/posts/282585) question we found that for a critical damped oscillation:

![Hi](https://electrical.codidact.com/uploads/YFDDpFztyswF1qeinfqvuZVj)

But if we integrate to find the voltage through the capacitor:

![Hi](https://electrical.codidact.com/uploads/ZCKF5vt61PecH38JsLeti9KW) 

the integral is always  a positive value which doesnt make any sense since the capacitor is being discharged.

What am I doing wrong here?Help appreciated!