# Response of a Series RLC Circuit

Discussion in 'Homework Help' started by p75213, Nov 29, 2011.

1. ### p75213 Thread Starter Active Member

May 24, 2011
70
0
Can anybody help with the attached exercise?
The answers are R=750 ohms, C=200 micro F, L=25H

To get R I tried Vc(t)/Il(t) but couldn't get 750 ohms.

To find C I have used the following equation.

It comes close to 200 micro F but not equal.

I am not sure how to get L

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Last edited: Nov 29, 2011
2. ### Vahe Member

Mar 3, 2011
75
9
p75213,

to calculate the capacitance, consider the following argument.

Depending on the direction of the inductor current and the capacitor voltage . We have the following relationship

The is necessary since the problem does not tell us if the inductor current is directed into the or the side of the capacitor voltage. Either way, this is fine. Now, evaluate the inductor current and capacitor voltage at a convenient time value, for example at . Now the above equation becomes,

We can find pretty easily. Just utilize the equations given in the problem statement with .

Now calculate the derivative of

Now calculate

Now we can calculate the numerical value of the capacitor

Of course, the only the positive value makes sense.

You could get the resistance and inductance values using the characteristic equation for the circuit. The characteristic equation for this circuit is . You can tell from the response that the natural frequencies (solutions of the characteristic equation for )) of the circuit are at . These are the factors multiplying on the exponentials. This means that the characteristic equation must be of the form in order to yield the correct natural frequencies. If we multiply out the polynomial we get

But this has to equal the characteristic equation as well; therefore, we have

Now we match the coefficients; therefore and . Now we solve for and knowing that the capacitor .

Hope it helps you out.

Best regards,
Vahe

Last edited: Dec 3, 2011
p75213 likes this.
3. ### p75213 Thread Starter Active Member

May 24, 2011
70
0
Thanks for that. I should have got C but I sure couldn't see R and L until you pointed it out.