Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Figure 21.55 shows how a bleeder resistor is used to discharge a capacitor after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? (b) How long will it take to reduce the voltage on the capacitor to $0.250 %$ (5% of 5%) of its full value once discharge begins? (c) If the capacitor is charged to a voltage V₀ through a 100-Ω resistance, calculate the time it takes to rise to 0.865V₀ (This is about two-time constants.)

(a) The time constant is $τ = 20 s$

(b) Time to reduce the voltage on the capacitor to $0.250 %$ is: $t = 119.8 s$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concept Introduction

A capacitor is an electrical energy storage device that operates in an electric field. It's a two-terminal passive electrical component. Capacitance is the term used to describe the effect of a capacitor.

Step 2: Time Constant

(a)

The following formula may be used to compute the time constant,

$τ = RC = (2.50 \times 10^{5} Ω) \times (8.0 \times 10^{5} F) = 20 s$

Step 3: Voltage Reduction

(b)

We will utilize anequation to determine how long it will take to drop the voltage on the capacitor to $0.250 %$ .

$V = V_{0} e^{(\frac{τ}{RC})} t = - [RC (\ln \frac{V}{V_{0}})] t = [(2.50 \times 10^{5} Ω) \times (8.0 \times 10^{- 5} F) \ln (0.0025)] t = 119.8 s$

Hence, the time to reduce the voltage on the capacitor to $0.250 %$ is $119.8 s$ .

Step 4: Rising Time of Capacitor

(c)

For charging, we'll use the following equation,

$V = V_{0} (1 - e^{- (\frac{t}{RC})}) t = - [RC (\ln (\frac{V_{0} - V}{V_{0}}))] t = [(100 Ω) \times (8.0 \times 10^{- 5} F) \ln (1 - 0.865)] t = 0.016 s$

Therefore, the time it takes to rise to 0.865V₀ is $0.016 s$ .

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College Physics (Urone)

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Short Answer

Step by Step Solution

Step 1: Concept Introduction

Step 2: Time Constant

Step 3: Voltage Reduction

Step 4: Rising Time of Capacitor

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College Physics (Urone)

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Short Answer

Step by Step Solution

Step 1: Concept Introduction

Step 2: Time Constant

Step 3: Voltage Reduction

Step 4: Rising Time of Capacitor

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