In the circuit shown in the figure below switch S1 has been

In the circuit shown in the figure below, switch S1 has been closed for a long enough time so that the current reads a steady 3.55 A. Suddenly, switch S2 is closed and S1 is opened at the same instant. (Assume L = 1.3 mH and C = 5.9 µF.)

(a) What is the maximum charge that the capacitor will receive?

mC

(b) What is the current in the inductor at this time?

A

Solution

a) The part of the circuit containing S2, L, & C can be interpreted as a lossless oscillator. Since it is lossless we can equate the maximum energy stored in the inductor to the max energy stored in the cap: 0.5*L*3.55^2 = 0.5*(Q^2)/C where Q is the maximum charge. Q = 3.55*sqrt(L*C) = 3.1 * 10^-4 C

b) this question is ambiguous. To what time does \'this time\' refer ? Is it the time at which the switches move, or the time at which the cap has its maximum charge. My guess is that it refers to \'the same instant\' - i.e the time at which the switches move - since no other time is mentioned. The answer to this is 3.55A. The current in the inductor at the time that the cap has its max charge is zero.