Solving LC Circuits: Time Interval Between Max Current & Voltage

[mm2424]

Homework Statement

The total energy stored in an LC circuit is 2J. The inductance is 10^-2 H and the capacitance is 100 μF. What is the time interval between a maximum current through the inductor and a maximum potential difference in the capacitor?

Homework Equations

T = 2∏/ω
ω = √(1/LC)

The Attempt at a Solution

I understand how the two above equations can be used to find T. However, in the answer key I have, it requires you to take the T you get and divide by 4 to find the time. I don't understand where this step comes in.

Also, is it possible to solve this question using the equation that tells us the charge on a capacitor (q = QV - e^(-t/RC)). I initially tried setting this up to find t when q = 0 and t when q = Q. However, is this not possible because we do know know and cannot find R? Or is there some other reason why using this equation won't work? Thanks!

 

[ehild]

It is a resonant LC circuit,without resistance. A similar equation you wrote (q = QV - e^(t/RC), which is not correct at all) would hold for a capacitor and resistor.
The current in the LC circuit changes with time as Imax sin (ωt), the voltage is U=±Umax cos(ωt) across any of the inductor and capacitor. The power stored in a capacitor is 1/2 CU², the same in the inductor is 1/2 L I². Plot U² and I² vs time. How many times during a period you get a maximum of either U² or I²?

ehild

 

[mm2424]

Oh, I see, thanks. Can you explain why we have to divide by 4 as the final step?

 

[ehild]

I edited my previous post, read it.

ehild

 

[mm2424]

Sorry, but this particular subject material is largely over my head. I can't really follow what you suggest I do. Is there another way to look at it? Alternatively, is it always true that one period includes 4 cycles, such that you always divide the period by 4 to find the time it takes to go from greatest charge on the capacitor to largest current? Sorry if I'm being annoying!

 

[ehild]

Why don't you plot U(t) and I(t)? When the current is maximum, the potential difference is zero, as U=LdI/dt. It will be maximum after pi//2 phase difference.

ehild