Question in the attachment A 7.32 µF capacitor is charged with a 95.8 V battery. Now the battery is disconnected, and the capacitor is connected in series to, a 8.68 mH resistanceless coil, a19.4 Q resistor and an open switch. At t = 0, the switch is closed. Find the energy, in µJ, stored in the capacitor at t = 0.708 ms.HINT : Is this circuit over, under or critically damped?

Answered: A 7.32 µF capacitor is charged with a…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question in the attachment

A 7.32 µF capacitor is charged with a 95.8 V battery. Now the battery is disconnected, and the capacitor is connected in series to, a 8.68 mH resistanceless coil, a
19.4 Q resistor and an open switch. At t = 0, the switch is closed. Find the energy, in µJ, stored in the capacitor at t = 0.708 ms.
HINT : Is this circuit over, under or critically damped?

Expert Solution

Step 1

Given: A charged capacitor is connected in series with a resistor and an inductor at t = 0 as shown in figure below:

Step 2

Order of the circuit is two, with characteristic equation roots given as $s_{1, 2} = - α \pm \sqrt{α^{2} - ω_{0}^{2}}$ .

Here,

$α = \frac{R}{2 L}, ω_{0} = \frac{1}{\sqrt{L C}} .$

Substituting the values,

$α = \frac{R}{2 L} = \frac{19.4}{2 \times 8.68 \times 10^{- 3}} = 1117.51, ω_{0} = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{8.68 \times 10^{- 3} \times 7.32 \times 10^{- 6}}} = 396.72 .$

$∵ α > ω_{0}$ , we have the overdamped case.

The voltage across capacitor after time t = 0, has a form

$v_{c} (t) = A e^{- s_{1} t} + B e^{- s_{2} t} .$

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