The maximum instantaneous value of current is 25 mA in this LC circuit.
a) What is the maximum value of charge separation on the capacitor?
b) How long does it take for all energy in one circuit element to be transferred to the other one?
a) Since there is no loss mechanism in this circuit (namely a resistor!), the energy in the inductor will be completely transferred to the capacitor and back repetitively. The energy in an inductor is given by (1/2)Li2; given the maximum vale of current 0.025 A, the maximum energy stored in the inductor will be 4.7 microjoules. That must then be the maximum energy in the capacitor, given by q2/2C; thus the maximum charge on the capacitor is 180 microcoulombs.
b) The angular frequency of the oscillation can be found from the reciprocal of the square root of the product of L and C. For this circuit the angular frequency is 138 rad/sec. This corresponds to a linear frequency of 22 Hz and a period of the oscillation equal to 46 ms. Keep in mind that the energy completely transforms from magnetic to energy in just one-fourth of the period, so the answer is 11 ms.