Answered: L Zmax S Figure P31.30 Problems 30 and…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

Why is the following situation impossible? The LC circuit as shown has L = 30.0 μH and C = 50.0 μF. The capacitor has an initial charge of 200 μC. The switch is closed, and the circuit undergoes undamped LC oscillations. At periodic instants, the energies stored by the capacitor and the inductor are equal, with each of the two components storing 250 μJ.

L
Zmax
S
Figure P31.30 Problems 30 and 32.
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Expert Solution

Step 1

The energy stored in the capacitor is given by the expression as shown below:

$E = \frac{1}{2} C V^{2}$

The voltage across the capacitor is given by the expression,

$Q = C V V = \frac{Q}{C} C = 50 μ F Q = 200 μ C V = \frac{200 \times 10^{- 6}}{50 \times 10^{- 6}} V o l t s V = 4 V o l t s$

Plugging the known values in the above expression,

$C = 50 μ F V = 4 V o l t s E = \frac{1}{2} C V^{2} E = \frac{1}{2} \times (50 \times 10^{- 6}) \times 4^{2} J E = 4 \times 10^{- 4} J E = 400 μ J$

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