| Line 37: | Line 37: | ||
8^2 - \frac{4}{2C} = 0\\ | 8^2 - \frac{4}{2C} = 0\\ | ||
64 = \frac{2}{C}\\ | 64 = \frac{2}{C}\\ | ||
| − | C = \frac{1}{32}\\ | + | '''C = \frac{1}{32}'''\\ |
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 13:51, 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
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