This problem concerns the electric circuit shown 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
Then, just as as a spring can have a damping force which affects its motion,
so can a circuit; this is introduced by the resistor, so that if the
resistance of the resistor is ,
If henry, ohm, and
farads, find a formula for the
charge when
(a)
and :
(b)
and :
You can earn partial credit on this problem.