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It all depends on the values of the components:If the system will very slowly decay until the energy of the system reaches 0. If the system undergoes something which will look like a part of...
Answer
#3: Post edited
by
MissMulan
·
2021-09-09T19:07:44Z (over 2 years ago)
- It all depends on the values of the components:If
- 
- the system will very slowly decay until the energy of the system reaches 0.
- If
- 
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- 
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- 
- so the the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- In order to find the equation of current of this RLC circuit we must be introduced to 2 things:
- Neper angular frequency -> a feature of damped systems
- In the case of parallel RLC circuit:
- 
- The equation of voltage of this critically damped system is:
- 
- where:
- 
- After the switch is closed:
- 
- and due to C1:
- 
- so the current through C1 is:
- 
- By substituting the values VC1(0+),iIC1(0+) and a we get:
- 
- This is the equation of the voltage of the top common node of C1,L1,R1 after the switch is closed.
- It all depends on the values of the components:If
- 
- the system will very slowly decay until the energy of the system reaches 0.
- If
- 
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- 
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- 
- 
- so the the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- In order to find the equation of current of this RLC circuit we must be introduced to 2 things:
- Neper angular frequency -> a feature of damped systems
- In the case of parallel RLC circuit:
- 
- The equation of voltage of this critically damped system is:
- 
- where:
- 
- After the switch is closed:
- 
- and due to C1:
- 
- so the current through C1 is:
- 
- By substituting the values VC1(0+),iIC1(0+) and a we get:
- 
- This is the equation of the voltage of the top common node of C1,L1,R1 after the switch is closed.
#2: Post edited
by
MissMulan
·
2021-09-08T16:36:23Z (over 2 years ago)
- It all depends on the values of the components:If
- 
- the system will very slowly decay until the energy of the system reaches 0.
- If
- 
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- 
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- 
- 
- so the the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- In order to find the equation of current of this RLC circuit we must be introduced to 2 things:
- Neper angular frequency -> a feature of damped systems
- In the case of parallel RLC circuit:
- 
- The equation of voltage of this critically damped system is:
- 
- where:
- 
- After the switch is closed:
- 
- and due to C1:
- 
- so the current through C1 is:
- 
- By substituting the values VC1(0+),iIC1(0+) and a we get:
- 
This is the equation of the voltage of the top branch of the loop consisting of C1,L1,R1 after the switch is closed.
- It all depends on the values of the components:If
- 
- the system will very slowly decay until the energy of the system reaches 0.
- If
- 
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- 
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- 
- 
- so the the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- In order to find the equation of current of this RLC circuit we must be introduced to 2 things:
- Neper angular frequency -> a feature of damped systems
- In the case of parallel RLC circuit:
- 
- The equation of voltage of this critically damped system is:
- 
- where:
- 
- After the switch is closed:
- 
- and due to C1:
- 
- so the current through C1 is:
- 
- By substituting the values VC1(0+),iIC1(0+) and a we get:
- 
- This is the equation of the voltage of the top common node of C1,L1,R1 after the switch is closed.
#1: Initial revision
by
MissMulan
·
2021-09-08T16:07:21Z (over 2 years ago)
It all depends on the values of the components:If  the system will very slowly decay until the energy of the system reaches 0. If  the system undergoes something which will look like a part of a oscillation and loses its energy very quickly If  it oscillates with decreasing amplitude until its energy reaches 0. In our case:   so the the system undergoes something which will look like a part of a oscillation and loses its energy very quickly In order to find the equation of current of this RLC circuit we must be introduced to 2 things: Neper angular frequency -> a feature of damped systems In the case of parallel RLC circuit:  The equation of voltage of this critically damped system is:  where:  After the switch is closed:  and due to C1:  so the current through C1 is:  By substituting the values VC1(0+),iIC1(0+) and a we get:  This is the equation of the voltage of the top branch of the loop consisting of C1,L1,R1 after the switch is closed.