The following problem concerns the electric
circuit in the figure below.
A charged capacitor connected to an inductor causes a current to flow
through the inductor until the capacitor is fully discharged. The current
in the inductor, in turn, charges up the capacitor until the capacitor is
fully charged again. If is the charge on the
capacitor at time , and is the current, then
If the circuit resistance is zero, then the charge and the
current in the circuit satisfy the differential
equation
where is the capacitance and is the inductance, so
The unit of
charge is the coulomb, the unit of capacitance the farad, the unit of
inductance the henry, the unit of current is the ampere, and time
is measured in seconds.
If henry and farad, find a formula for if
(a)
and :
(a)
and :
You can earn partial credit on this problem.