### RLC Circuits

An *LC* circuit has an inductance of 3.0 mH and a
capacitance of 10 mF.
Calculate (a) the angular frequency and (b) the period of oscillation. (c) At
time *t* = 0 the capacitor is charged to 200 mC,
and the current is zero. Sketch roughly the charge on the capacitor as a
function of time

A single loop circuit consists of a 7.22 W
resistor, a 12.3 H inductor, and a 3.18 mF
capacitor. Initially, the capacitor has a charge of 6.31 mC
and the current is zero. Calculate the charge on the capacitor *N* complete
cycles later for *N* = 5, 10, and 100.

How much resistance *R* should be connected to an inductor *L* = 220
mH and capacitor *C* = 12 mF
in series in order that the maximum charge on the capacitor decays to 99% of its
initial value in 50 cycles?