capacitor with an
initial charge of 10 mC. The resistance of the circuit is negligible. Let the
instant the circuit is closed be 
.
(a)
What is the total energy stored initially? Is it conserved during LC
oscillations?
(b)
What is the natural frequency of the circuit?
(e)
At what time is the energy stored
(i)
completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic
(i.e., stored in the inductor)?
(d)
At what times is the total energy- shared equally between the inductor and the
capacitor?
Answer:
(a) Total initial
energy
Yes,
if R = 0 then sum of energies for L and C is conserved.
(b)
Using 
we get
and
or 
(c)
Using 
and 
,
we get
(i)
Stored electrical energy at 
and
(iii)
Electric energy as zero and purely magnetic energy at 
Here
(d)
The energy is shared equally between inductor and capacitor at 
because.
Energy,
If 
then 
then
of the total
energy.
(e)
Total initial energy of 1 J will be lost as heat due to Joule?s heating effect
in the resistor.
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