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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
- It all depends on the values of the components:If
- ![](https://electrical.codidact.com/uploads/8ym42jU8HUER4jr6uEFSL2QW)
- the system will very slowly decay until the energy of the system reaches 0.
- If
- ![](https://electrical.codidact.com/uploads/mL9YkvUSVf8BH1MW96VuTu2V)
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- ![](https://electrical.codidact.com/uploads/dBSd36PuPH6yJ84shk7qdTZW)
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- ![](https://electrical.codidact.com/uploads/xqBmzivFipgBcRrLYvTGdEMr)
- ![](https://electrical.codidact.com/uploads/fwzhAAuRZbiuXVPvAq3HP5Ae)
- it will very slowly decay without any oscillation.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 the series RLC circuit it is:
- ![](https://electrical.codidact.com/uploads/D2iMorYukryhtQqg3bXhY92V)
- The natural angular frequency -> the frequency response of the system under no damping
- In a RLC circuit it is equal to:
- ![Image alt text](https://electrical.codidact.com/uploads/RhZNfiqZx9ZGmHSnftjnLHU3)
- The equation of current of this overdamped system takes this form:
- ![Image alt text](https://electrical.codidact.com/uploads/u2cWGVD5oMCCR6gkzbvwqrc6)
- where :
- ![](https://electrical.codidact.com/uploads/ZRDLjwdRtkrFGKfr9bTVtt6G)
- (1)
- and:
- ![](https://electrical.codidact.com/uploads/imNfVLKa1zjacV1MTP8iWjUh)
- Now lets go calculate s1 and s2:
- ![](https://electrical.codidact.com/uploads/qBbadovLpxGormHJeBW61wWb)
- After the switch is closed:
- ![Image alt text](https://electrical.codidact.com/uploads/wNSsrYNSB1hu6UgorJnL7Z8i)
- and due to L1:
- ![](https://electrical.codidact.com/uploads/oCDeSgowdkLP5a5xyeveXy3s)
- so the voltage between L1 is:
- ![](https://electrical.codidact.com/uploads/1YMPV5DcPvqiHdw8FoB8mDQU)
- By substituting the values of s1,s2 VL1(0+),L1 and IL1(0+) to (1) and solving the system we get:
- ![](https://electrical.codidact.com/uploads/rDVwMFUgTWfrNYEAW3hoabfv)
This is the equation of the current of the loop consisting of C1,L1,R2 after the switch is closed.
- It all depends on the values of the components:If
- ![](https://electrical.codidact.com/uploads/8ym42jU8HUER4jr6uEFSL2QW)
- the system will very slowly decay until the energy of the system reaches 0.
- If
- ![](https://electrical.codidact.com/uploads/mL9YkvUSVf8BH1MW96VuTu2V)
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- ![](https://electrical.codidact.com/uploads/dBSd36PuPH6yJ84shk7qdTZW)
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- ![](https://electrical.codidact.com/uploads/xqBmzivFipgBcRrLYvTGdEMr)
- ![](https://electrical.codidact.com/uploads/fwzhAAuRZbiuXVPvAq3HP5Ae)
- it will very slowly decay without any oscillation.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 the series RLC circuit it is:
- ![](https://electrical.codidact.com/uploads/D2iMorYukryhtQqg3bXhY92V)
- The natural angular frequency -> the frequency response of the system under no damping
- In a RLC circuit it is equal to:
- ![Image alt text](https://electrical.codidact.com/uploads/RhZNfiqZx9ZGmHSnftjnLHU3)
- The equation of current of this overdamped system takes this form:
- ![Image alt text](https://electrical.codidact.com/uploads/u2cWGVD5oMCCR6gkzbvwqrc6)
- where :
- ![](https://electrical.codidact.com/uploads/ZRDLjwdRtkrFGKfr9bTVtt6G)
- (1)
- and:
- ![](https://electrical.codidact.com/uploads/imNfVLKa1zjacV1MTP8iWjUh)
- Now lets go calculate s1 and s2:
- ![](https://electrical.codidact.com/uploads/qBbadovLpxGormHJeBW61wWb)
- After the switch is closed:
- ![Image alt text](https://electrical.codidact.com/uploads/wNSsrYNSB1hu6UgorJnL7Z8i)
- and due to L1:
- ![](https://electrical.codidact.com/uploads/oCDeSgowdkLP5a5xyeveXy3s)
- so the voltage between L1 is:
- ![](https://electrical.codidact.com/uploads/1YMPV5DcPvqiHdw8FoB8mDQU)
- By substituting the values of s1,s2 VL1(0+),L1 and IL1(0+) to (1) and solving the system we get:
- ![](https://electrical.codidact.com/uploads/rDVwMFUgTWfrNYEAW3hoabfv)
- This is the equation of the current of the loop consisting of C1,L1,R1 after the switch is closed.
#2: Post edited
- It all depends on the values of the components:If
- ![](https://electrical.codidact.com/uploads/8ym42jU8HUER4jr6uEFSL2QW)
- the system will very slowly decay until the energy of the system reaches 0.
- If
- ![](https://electrical.codidact.com/uploads/mL9YkvUSVf8BH1MW96VuTu2V)
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- ![](https://electrical.codidact.com/uploads/dBSd36PuPH6yJ84shk7qdTZW)
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
![](https://electrical.codidact.com/uploads/6dxozgLnSfUfFf7antzszExj)since:- ![](https://electrical.codidact.com/uploads/fwzhAAuRZbiuXVPvAq3HP5Ae)
- it will very slowly decay without any oscillation.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 the series RLC circuit it is:
![](https://electrical.codidact.com/uploads/pnofzBNJ1DicX31dBBRPRvvh)- The natural angular frequency -> the frequency response of the system under no damping
- In a RLC circuit it is equal to:
- ![Image alt text](https://electrical.codidact.com/uploads/RhZNfiqZx9ZGmHSnftjnLHU3)
- The equation of current of this overdamped system takes this form:
- ![Image alt text](https://electrical.codidact.com/uploads/u2cWGVD5oMCCR6gkzbvwqrc6)
- where :
- ![](https://electrical.codidact.com/uploads/ZRDLjwdRtkrFGKfr9bTVtt6G)
- (1)
- and:
- ![](https://electrical.codidact.com/uploads/imNfVLKa1zjacV1MTP8iWjUh)
- Now lets go calculate s1 and s2:
- ![](https://electrical.codidact.com/uploads/qBbadovLpxGormHJeBW61wWb)
- After the switch is closed:
- ![Image alt text](https://electrical.codidact.com/uploads/wNSsrYNSB1hu6UgorJnL7Z8i)
- and due to L1:
- ![](https://electrical.codidact.com/uploads/oCDeSgowdkLP5a5xyeveXy3s)
- so the voltage between L1 is:
- ![](https://electrical.codidact.com/uploads/1YMPV5DcPvqiHdw8FoB8mDQU)
By substituting the values of s1,s2 VL1(0+),L1 to (1) and solving the system we get:- ![](https://electrical.codidact.com/uploads/rDVwMFUgTWfrNYEAW3hoabfv)
- This is the equation of the current of the loop consisting of C1,L1,R2 after the switch is closed.
- It all depends on the values of the components:If
- ![](https://electrical.codidact.com/uploads/8ym42jU8HUER4jr6uEFSL2QW)
- the system will very slowly decay until the energy of the system reaches 0.
- If
- ![](https://electrical.codidact.com/uploads/mL9YkvUSVf8BH1MW96VuTu2V)
- the system undergoes something which will look like a part of a oscillation and loses its energy very quickly
- If
- ![](https://electrical.codidact.com/uploads/dBSd36PuPH6yJ84shk7qdTZW)
- it oscillates with decreasing amplitude until its energy reaches 0.
- In our case:
- ![](https://electrical.codidact.com/uploads/xqBmzivFipgBcRrLYvTGdEMr)
- ![](https://electrical.codidact.com/uploads/fwzhAAuRZbiuXVPvAq3HP5Ae)
- it will very slowly decay without any oscillation.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 the series RLC circuit it is:
- ![](https://electrical.codidact.com/uploads/D2iMorYukryhtQqg3bXhY92V)
- The natural angular frequency -> the frequency response of the system under no damping
- In a RLC circuit it is equal to:
- ![Image alt text](https://electrical.codidact.com/uploads/RhZNfiqZx9ZGmHSnftjnLHU3)
- The equation of current of this overdamped system takes this form:
- ![Image alt text](https://electrical.codidact.com/uploads/u2cWGVD5oMCCR6gkzbvwqrc6)
- where :
- ![](https://electrical.codidact.com/uploads/ZRDLjwdRtkrFGKfr9bTVtt6G)
- (1)
- and:
- ![](https://electrical.codidact.com/uploads/imNfVLKa1zjacV1MTP8iWjUh)
- Now lets go calculate s1 and s2:
- ![](https://electrical.codidact.com/uploads/qBbadovLpxGormHJeBW61wWb)
- After the switch is closed:
- ![Image alt text](https://electrical.codidact.com/uploads/wNSsrYNSB1hu6UgorJnL7Z8i)
- and due to L1:
- ![](https://electrical.codidact.com/uploads/oCDeSgowdkLP5a5xyeveXy3s)
- so the voltage between L1 is:
- ![](https://electrical.codidact.com/uploads/1YMPV5DcPvqiHdw8FoB8mDQU)
- By substituting the values of s1,s2 VL1(0+),L1 and IL1(0+) to (1) and solving the system we get:
- ![](https://electrical.codidact.com/uploads/rDVwMFUgTWfrNYEAW3hoabfv)
- This is the equation of the current of the loop consisting of C1,L1,R2 after the switch is closed.
#1: Initial revision
It all depends on the values of the components:If ![](https://electrical.codidact.com/uploads/8ym42jU8HUER4jr6uEFSL2QW) the system will very slowly decay until the energy of the system reaches 0. If ![](https://electrical.codidact.com/uploads/mL9YkvUSVf8BH1MW96VuTu2V) the system undergoes something which will look like a part of a oscillation and loses its energy very quickly If ![](https://electrical.codidact.com/uploads/dBSd36PuPH6yJ84shk7qdTZW) it oscillates with decreasing amplitude until its energy reaches 0. In our case: ![](https://electrical.codidact.com/uploads/6dxozgLnSfUfFf7antzszExj) since: ![](https://electrical.codidact.com/uploads/fwzhAAuRZbiuXVPvAq3HP5Ae) it will very slowly decay without any oscillation.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 the series RLC circuit it is: ![](https://electrical.codidact.com/uploads/pnofzBNJ1DicX31dBBRPRvvh) The natural angular frequency -> the frequency response of the system under no damping In a RLC circuit it is equal to: ![Image alt text](https://electrical.codidact.com/uploads/RhZNfiqZx9ZGmHSnftjnLHU3) The equation of current of this overdamped system takes this form: ![Image alt text](https://electrical.codidact.com/uploads/u2cWGVD5oMCCR6gkzbvwqrc6) where : ![](https://electrical.codidact.com/uploads/ZRDLjwdRtkrFGKfr9bTVtt6G) (1) and: ![](https://electrical.codidact.com/uploads/imNfVLKa1zjacV1MTP8iWjUh) Now lets go calculate s1 and s2: ![](https://electrical.codidact.com/uploads/qBbadovLpxGormHJeBW61wWb) After the switch is closed: ![Image alt text](https://electrical.codidact.com/uploads/wNSsrYNSB1hu6UgorJnL7Z8i) and due to L1: ![](https://electrical.codidact.com/uploads/oCDeSgowdkLP5a5xyeveXy3s) so the voltage between L1 is: ![](https://electrical.codidact.com/uploads/1YMPV5DcPvqiHdw8FoB8mDQU) By substituting the values of s1,s2 VL1(0+),L1 to (1) and solving the system we get: ![](https://electrical.codidact.com/uploads/rDVwMFUgTWfrNYEAW3hoabfv) This is the equation of the current of the loop consisting of C1,L1,R2 after the switch is closed.