# LC circuit: finding the time interval between maximum potential and maximum current

## 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?

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!

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ehild
Homework Helper

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

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

ehild
Homework Helper

I edited my previous post, read it.

ehild

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
Homework Helper

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

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