# LC circuit

Discussion in 'Electronics Homework Help' started by Daedalus, Nov 11, 2018.

1. ### Daedalus

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Nov 11, 2018
I have the LC circuit of the figure: At initial time C2 has a charge Q2, and C1 has Q1=0. I am asked to find the voltage across C2, and the current at any other time.

So what I did was first to consider the equivalent circuit, with Then I have: So I have, using the initial condition: Then, to find the voltage across C2, I've used (which I'm not sure if this right):

q(t)=Q1(t)+Q2(t), the total charge should be the sum of charges in both capacitors. And then I used that the charge should be related to the voltage as: Q1=C1V, Q2=C2V, where I am assuming that the voltage drop is the same in both capacitors (I'm not sure if that is correct). Then I have: So, is this correct?

Or should I consider, instead of what I did: If I use the last equation, I get: I think this last result is correct, because I am not doing any ad hoc assumption. But at the same time, I find a different current that the one I obtain for the equivalent circuit. Shouldn't the current be the same across the capacitor than for the equivalent circuit?

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Last edited: Nov 11, 2018
2. ### Harald KappModeratorModerator

10,025
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Nov 17, 2011
Assuming switch S is closed at t=0 ?

3. ### Daedalus

3
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Nov 11, 2018
Yes, sorry. I might have an error sign in the last equations.

4. ### Ratch

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Mar 10, 2013
Tsk, tsk, you really are lost in the wilderness. You cannot combine the two capacitors because only one cap has a charge imbalance on it. How is that going to affect the "equivalent" capacitor? So, one cap has a voltaqe across it and the other cap does not. Do you know what that voltage is? Find the current in the loop, then you can easily calculate the voltage across any of the circuit elements. Since you are asked to solve the equations symbolically, you are in for a long derivation. I am going to use Laplace transforms to simplify the path to the solution. By the way, did you check and proof the quality of your embedded images after the first one in your post? All I see is garbage.

The loop expressed in Laplace terms is: Solving for Is we obtain: Finding the inverse we get a real time current of : Normalizing the circuit parameters we can simplify and plot the current.   From the simplified equation we can see the amplitude is 1/sqrt(2) = 0.707 and the period is 2 Pi/sqrt(2) = 4.44 seconds. You can expect a sine wave for the current because there is both capacitance and inductance in the circuit. The wave will last forever because no resistance is present. Now that you know the current, can you find the voltages across each circuit element?

Ratch

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5. ### Daedalus

3
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Nov 11, 2018
Hi. Thanks a lot. I did check the images, they look fine in my computer after I logged in (I'm in a different place than when I wrote the post, in both systems I use ubuntu and mozilla ff, however the forums should enable the use of latex!). I didn't expected to be so complicated! it was supposed to be an exercise for students learning a very short course in electromagnetism! I will try to avoid laplace transforms, because the student don't have that backgrounds (first year at university level).

Thanks again!  