Question

2. An ideal inductor with inductance L and an ideal capacitor with capacitance C are connected in series with a battery with voltage and a switch. Att 0 the switch is closed. In this scenario, the charge on the capacitor will oscillate sinusoidally but will have a DC offset. It can be expressed in general using three parameters (Ao, Ai, and A2) with the following. q(t) AA cos(ut)A2 sin(ut) where wis the natural frequency of the circuit. Note also that Ag is the DC offset. (a) Use the fact that at t-0 the charge on the capacitor is zero to find a relation between Ag and A (b) Use the fact that at t 0 the current in the circuit is zero to determine Ap. (c) Use the fact that at all times the net voltage drop across the capacitor and inductor must equal the voltage of the battery (Vo+Vi- V) to determine Ao (d) On the axes below, carefully sketch a graph of one cycle of the charge on the capacitor as a function of time. Indicate the DC offset and the amplitude of oscillation. 9(t)

Answer 1

1 ~ da,ーー4,0 sinat A a@çat 1(0) 。 dt drob across the : voutoae drap acrossthe LC

се ce 2 a CE