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 a and have been there for a long time.Assume all wires and connections have negligible resistance. Here are the known values: E = 9.00 V, C=135µF, R1 = R2 = 4.32 ohms,R3=7.68 Ohms, L1 = 52.1 mH, L2 = 46.7 mH a. 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 on the capacitor than in the initial situation.” b. 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. c. Now suppose that switch 2 is moved to position 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 L2 has decayed (disappeared)? 1. An ideal battery is connected as shown to three resistors, switch 2 switch 1 Ra one capacitor and two inductors. Both switches were set initially to position a and have been there for a long time. Assume all wires and connections have negligible resistance. Here are the know values: E 9.00 V C 135 uF R, 4.32 2 R, 7.68 2 55.1 mH 46.7 mH a. Now switch l is moved to its position b. Evaluate the following statement (TIFIN) and fully justify your answer. "With switch 1 in position b,there is less energy stored on the capacitor than in the initial situation." b. 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 c. Now suppose that switch 2 is moved to position 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, has decayed (disappeared)?

Explanation / Answer

a.

False

the energy stored in the capacitor will remain same as moving the switch 1 from a to b does not change the Voltage across the capacitor since the battery is attached in parallel with the capacitor.

Energy = (0.5) CE2

Since C and E remain same , energy remains same

b)

i = current through inductor = E/R2 = 9/4.32 = 2.1 A

energy stored by indutor = (0.5) L i2 = (0.5) (0.0521) (2.1)2 = 0.115 J

energy stored in capacitor = (0.5) CE2 = (0.5) (135 x 10-6) (9)2 = 0.0055 J

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