An ideal battery is connected as shown to three resistors, one capacitor and two

Question

An ideal battery is connected as shown to three resistors, one capacitor and two inductors. Both switches were set initially to position and have been there for a long time. Assume all wires and connections have negligible resistance. Here the known values: epsilon = 9.00 V C = 135 mu F R_1 = R_2 = 4.32 Ohm R_3 = 7.68 Ohm L_1 = 52.1 mH, L_2 = 46.7 mH Now switch 1 is moved to its position b. evaluate the following statement (T/F/N) and fully justify your answer. "With switch 1 in position b, there is less energy stored in the capacitor than in the initial situation? Assuming switch 1 has now been in position b for a long time (with switch 2 still in position a), calculate the total energy stored in the capacitor and inductors. Now suppose that switch 2 is moved to positive b. then at some later moment, switch 1 is opened (moved back from position b to position a). Measured from that moment: In the time required for the oscillation in the LC circuit to undergo one full cycle, what percentage of the initial current in L_2 has decayed (disappeared)?

Explanation / Answer

a)   The following statement is True .

b)   Total energy stored =   1/2CV2 + 1/2LI2

                                      = (1/2 * 135 * 10-6 * 9 * 9) + (1/2 * 46.7 * 10-3 * 0.51 * 0.51)

                                     =    0.01154 J

c)    % of initial current decayed =     (0.325/0.51) * 100

                                                    = 63.72 %

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