# What is the capacitance of the circuit problem.

1. Dec 2, 2009

### tag16

1. The problem statement, all variables and given/known data
An LC circuit consists of a 1mH inductor. The capacitor is fully charged. After 2.1 ms,
the energy in the capacitor is ½ of its original value. What is the capacitance of the
circuit?

2. Relevant equations
(Q/C)+ L(d^2Q/dt^2)=0

d^2Q/dt^2= -(1/LC)Q

3. The attempt at a solution

I found the above equations in my physics book but I don't know what Q would be (it says that the capacitor is fully charged but it doesn't give an actual number), or how to get into a C= ? format in order to find the capacitance. Also I'm not even sure these are the formulas I need for this problem and if they're not then I have no idea what to do.

2. Dec 2, 2009

### rolisp

Re: capacitance

you can try to solve the task using Thomson's formula T=2*П * root of L*C
as i understood there is given that after 2,1 ms the capacitor is half discharged and it means that it will be fully dischardged after 4,2 ms, that is 4,2*10^-3 s - it is full period of time.
transforming the formula C= (T^2) / (2^2 * П^2 * L) and the result is 4,4 micro farads.

3. Dec 2, 2009

### nasu

Re: capacitance

The charge varies with time according to a cosine function - Q=QoCos(wt)
w is the angular frequency.
From the fact that is 1/2 from the maximum at t=2.1 ms you can find w.