00:01
Hi there, so for this problem, we're told that for the time equals to zero, the charge is a charge that we're going to label as q -0, and the current is just zero.
00:15
So with that said, for part a of this problem, we are asked about at the first moment when the energy is shared equally by the inductor and the capacitor.
00:26
What is the charge on the capacitor? okay, then for this, we just need to...
00:43
So the energy store in a capacitor, we know that the energy store, is just equal to the initial charge to the square this divided by two times the capacitance.
00:57
Now, since the energy is stirred equally by the inductor and the capacitor, the new energy stored by the capacitor, let's label this new, is equal to the energy divided by a capacitor, so that will be then, we substitute that in here, we will obtain that that is the initial charge to the square d is divided by four times the capacitance.
01:25
Now for a charge queue store in the capacitor, the energy store is then given.
01:34
So this new energy is then the charge due to the square this divided by two times the capacitance.
01:43
So what we are going to do is to equal these two expressions together.
01:50
So when we do that, we obtain the following.
01:53
The initial charge to the square this divided by four times the capacitance, and then this is equal to the charge q to the square this divided by two times the capacitance.
02:07
Then, solving in here for the charge q, that is equal to the initial charge and this divided by the square root of 2.
02:22
So that's the solution.
02:26
So at the first moment when the energy is shared equally by the inductor and the capacitor, the charge of the capacitor is q squared divided by the square root of 2...