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| − | [[Category: | + | [[Category:ECE201]] |
| + | [[Category:ECE]] | ||
| + | [[Category:ECE201Spring2015Peleato]] | ||
| + | [[Category:circuits]] | ||
| + | [[Category:linear circuits]] | ||
| + | [[Category:problem solving]] | ||
| − | = | + | =Critically Damped Practice= |
| + | <center><font size= 4> | ||
| + | '''Practice question for [[ECE201]]: "Linear circuit analysis I" ''' | ||
| + | </font size> | ||
| + | By: Chinar Dhamija | ||
| + | Topic: Critically Damped Second Order Equation | ||
| − | + | </center> | |
| + | ---- | ||
| + | ==Question== | ||
| + | Find the value for C that will make the zero input response critically damped with roots at -4. | ||
| + | [[File:ECE201P6.png|500px|center]] | ||
| + | ---- | ||
| + | ---- | ||
| + | ===Answer === | ||
| + | For a response to be critically damped we know that:<br /> | ||
| + | <math>b^2 - 4c = 0</math><br /> | ||
| + | The next step would be to simplify the circuit as shown in the image below. Once simplified it becomes a parallel RLC circuit where we know:<br /> | ||
| + | <math> b = \frac{1}{RC} </math> and <math> c = \frac{1}{LC} </math> | ||
| + | [[File:ECE201P6_1.png|500px|center]] | ||
| + | Since the root was given to be -4 we can find b.<br /> | ||
| + | <math> \frac{-b}{2} = s </math> so we get: <math> \frac{-b}{2} = -4 </math> therefore b = 8. <br /> | ||
| + | Once we know b we can use the critically damped equation to solve for C.<br /> | ||
| + | <math>\begin{align} | ||
| + | 8^2 - \frac{4}{2C} = 0\\ | ||
| + | 64 = \frac{2}{C}\\ | ||
| + | C = \frac{1}{32}\\ | ||
| + | \end{align} | ||
| + | </math> | ||
| − | [[ 2015 Spring ECE 201 Peleato|Back to 2015 Spring ECE 201 Peleato]] | + | ---- |
| + | ==Questions and comments== | ||
| + | If you have any questions, comments, etc. please post them below | ||
| + | *Comment 1 | ||
| + | **Answer to Comment 1 | ||
| + | *Comment 2 | ||
| + | **Answer to Comment 2 | ||
| + | ---- | ||
| + | [[2015 Spring ECE 201 Peleato|Back to 2015 Spring ECE 201 Peleato]] | ||
| + | |||
| + | [[ECE201|Back to ECE201]] | ||
Latest revision as of 14:51, 2 May 2015
Critically Damped Practice
Practice question for ECE201: "Linear circuit analysis I"
By: Chinar Dhamija
Topic: Critically Damped Second Order Equation
Question
Find the value for C that will make the zero input response critically damped with roots at -4.
Answer
For a response to be critically damped we know that:
$ b^2 - 4c = 0 $
The next step would be to simplify the circuit as shown in the image below. Once simplified it becomes a parallel RLC circuit where we know:
$ b = \frac{1}{RC} $ and $ c = \frac{1}{LC} $
Since the root was given to be -4 we can find b.
$ \frac{-b}{2} = s $ so we get: $ \frac{-b}{2} = -4 $ therefore b = 8.
Once we know b we can use the critically damped equation to solve for C.
$ \begin{align} 8^2 - \frac{4}{2C} = 0\\ 64 = \frac{2}{C}\\ C = \frac{1}{32}\\ \end{align} $
Questions and comments
If you have any questions, comments, etc. please post them below
- Comment 1
- Answer to Comment 1
- Comment 2
- Answer to Comment 2
