Q. 66 66. II FIGURE P30.66 shows the c... [FREE SOLUTION]

Chapter 30: Q. 66 (page 873)

66. II FIGURE P30.66 shows the current through a $10 mH$ inductor. Draw a graph showing the potential difference $螖 V_{L}$ across the inductor for these $6 ms$ .

Short Answer

Expert verified

The potential difference across the inductor is

$\begin{array}{l} 螖 V_{L} = 鈭� 10 Vfor 0 ms < t < 2 ms \\ 螖 V_{L} = 0 痴鈥勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌刦辞谤 2 ms < t < 3 ms \\ 螖 V_{L} = 20 痴鈥勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌刦辞谤 3 ms < t < 5 ms \\ 螖 V_{L} = 0 痴鈥勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨赌刦辞谤 t > 5 ms \end{array}$

Step by step solution

Step 1. Introduction

It is given that the value of inductor, $L = 10 mH = 10 脳 10^{鈭� 3} H$

We have potential difference across the inductor as $螖 V_{L} = 鈭� L \frac{d I}{d t}$

Step 2. Explanation

From $t = 0 ms$ to $t = 2 ms$ , current $I$ changes from $0 鈥凙鈥则辞鈥�2础$ .

$\begin{array}{l} \frac{d I}{d t} = \frac{(2 A 鈭� 0 A)}{(2 ms 鈭� 0 ms)} = \frac{2 A}{(2 ms) (10^{鈭� 3} s / ms)} = 1000 A / s \\ 螖 V_{L} = 鈭� (10 脳 10^{鈭� 3} H) (1000 A / s) = 鈭� 10 V \end{array}$

Step 3.

From $t = 2 ms$ to role="math" $t = 3 ms,$ role="math" $I$ remains constant

Therefore voltage becomes zero.

Step 3.

Now from $t = 3 ms$ to $5 ms$ , the current decreases from $2 A$ to $鈭� 2 A$

$\begin{array}{l} \frac{d I}{d t} = \frac{(鈭� 2 A 鈭� 2 A)}{(5 ms 鈭� 3 ms)} \\ = \frac{鈭� 4 A}{(2 ms) (10^{鈭� 3} s / ms)} \\ = 鈭� 2000 A / s \end{array}$

So, the inductor voltage is

$螖 V_{L} = 1 (10 脳 10^{鈭� 3} H) (鈭� 2000 A / s) = 20 V$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

66. II FIGURE P30.66 shows the current through a $10 mH$ inductor. Draw a graph showing the potential difference $螖 V_{L}$ across the inductor for these $6 ms$ .

Short Answer

Step by step solution

Step 1. Introduction

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Modern Physics

Thermodynamics

Fundamentals of Physics

Magnetism and Electromagnetic Induction

Wave Optics

Study anywhere. Anytime. Across all devices.

91影视

66. II FIGURE P30.66 shows the current through a10mH inductor. Draw a graph showing the potential difference螖VL across the inductor for these6ms .

Short Answer

Step by step solution

Step 1. Introduction

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Modern Physics

Thermodynamics

Fundamentals of Physics

Magnetism and Electromagnetic Induction

Wave Optics

Study anywhere. Anytime. Across all devices.

66. II FIGURE P30.66 shows the current through a $10 mH$ inductor. Draw a graph showing the potential difference $螖 V_{L}$ across the inductor for these $6 ms$ .