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Full Wave Rectification

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Question

Show that in the free oscillations of an LC circuits, the sum of energies stored in the capacitor and the inductor is constant in time

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Q. A LC-circuit contains a

20 m H

50 μ F

capacitor with an initial charge of

10 m C

. The resistance of the circuit is negligible. Let the instant the circuit is closed be

t = 0

(a) What is the total energy stored initially. Is it conserved during the LC-oscillations?
(b) What is the natural frequency of the circuit?
(c) At what times is the energy stored?
(i) completely electrical (ie., stored in the capacitor)?
(ii) completely magnetic (i.e., stored in the inductor)?
(d) At what time is the total energy shared equally between the inductor and the capacitor

L C

circuit contains a

20 m H

50 μ F

capacitor with an initial charge of

10 m C

. The resistance of the circuit is negligible. Let the instant circuit is closed be at

t = 0

What is the total energy stored initial? Is it conserved during the

L C

Q. In an oscillating

L C

circuit, the total stores energy is

U

and the maximum charge on the capacitor is

Q

. When the charge on the capacitor is

Q / 2

, the energy stored in the inductor is :

Q. An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible.Let the instant the circuit is closed be t = 0. (a) What is the total energy stored initially? Is it conserved during LC oscillations? (b) What is the natural frequency of the circuit? (c) At what time is the energy stored (i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)? (d) At what times is the total energy shared equally between the inductor and the capacitor? (e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

Q. An LC circuit contains a 20 mH inductor and a 50

μ

F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.(a) What is the total energy stored initially? Is it conserved during LC oscillations?

(b) What is the natural frequency of the
circuit?

(c) At what time is the energy stored

(i) completely electrical (i.e., stored in the capacitor)?

(ii) completely magnetic (i.e. stored in the inductor)?

(d) At what times is the total energy shared
equally between the inductor and the capacitor?

(e) If a resistor is inserted in the circuit,

how much energy is eventually dissipated as heat?

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