7.12 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?

5 Views|Posted 8 months ago

Asked by Shiksha User

1 Answer

Sort by:

Answered by

8 months ago

7.12 Inductance of the Inductor, L = 20 mH = 20 $*$ $10^{- 3}$ H

Capacitance of the capacitor, C = 50 $μ F$ = 50 $* 10^{- 6}$ F

Initial charge of the capacitor, Q = 10 mC = 10 $* 10^{- 3}$ C

The total energy stored initially at the circuit is given as

E = $\frac{1}{2}$ $* \frac{Q^{2}}{C}$ = $\frac{1}{2}$ $* \frac{{(10 * 10^{- 3})}^{2}}{50 * 10^{- 6}}$ = 1 J

Hence, the total energy stored in the LC circuit will be conserved because ther

Upvote

Taking an Exam? Selecting a College?

Get authentic answers from experts, students and alumni that you won't find anywhere else.

On Shiksha, get access to

66K

Colleges

1.2K

Exams

6.8L

Reviews

1.8M

Answers

Search from Shiksha's 1 lakh+ Topics

See what others like you are asking & answering