Q. 67 67. II FIGURE P30.67 shows the p... [FREE SOLUTION]

91影视

Chapter 30: Q. 67 (page 874)

67. II FIGURE P30.67 shows the potential difference across a potential difference across a $50 mH$ inductor. The current through the inductor at $t = 0 s$ is $0.20 A$ . Draw a graph showing the current through the inductor from $t = 0 s$ to $t = 40 ms$

Short Answer

Expert verified

The following graph between current and time is

Step by step solution

Step 1. Given information

We have $螖 r_{L} = 鈭� 1 V_{for} 0 ms < t < 10 ms$

$\begin{array}{l} So \\ 鈭� L \frac{d I}{d t} = 鈭� 1 V \\ \frac{d I}{d t} = \frac{1 V}{50 mH} = 20 A / s \end{array}$

$\begin{array}{l} d I = (20 A / s) d t I = (20 A / s) t + c \\ Butat t = 0, I = 0.2 A \\ 0.2 A = 0 + c \end{array}$

$\begin{array}{l} I = (20 A / s) t + 0.2 础鈥勨赌勨赌勨赌勨赌勨赌勨赌� \\ At t = 10 ms = 10 脳 10^{鈭� 3} s \\ I = (20 A / s) (10 脳 10^{鈭� 3} s) + 0.2 A \\ = 0.2 A + 0.2 A \\ = 0.4 A \end{array}$

Explanation

From $t = 0 ms$ to $t = 10 ms$ current increase from $0.2 A$ to $0.4 A$ .

From the figure below, for $螖 V_{L} = 0$

for $10 ms < t < 20 ms$ $I = 0.4 A$ $10 ms < t < 20 ms$

Now $螖 V_{L} = 2 V_{for} 20 ms < t < 30 ms$

$\begin{array}{l} 鈭� L \frac{d I}{d t} = 2 V \\ \frac{d I}{d t} = \frac{鈭� 2 V}{50 mH} = 鈭� 40 A / s (or) \\ d I = (鈭� 40 A / s) d t \\ I = (鈭� 40 A / s) t + c \\ At t = 20 ms, \\ I = 0.4 A \\ 0.4 A = (鈭� 40 A / s) (20 ms) (10^{鈭� 3} s / ms) + c \\ 鈬� 0.4 A = 鈭� 0.8 A + c \\ 鈬� c = 1.2 A I \\ = (鈭� 40 A / s) t + 1.2 A \end{array}$

Now At

$t = 30 尘蝉鈥�=鈥� 30 脳 10^{鈭� 3} s$

$\begin{array}{l} I = (鈭� 40 A / s) (30 脳 10^{鈭� 3} s) + 1.2 A \\ = 鈭� 1.2 A + 1.2 A \\ = 0 A \end{array}$

Current decreases from $0.4 A_{to} 0 A_{in}$ the time $20 ms < t < 30 ms$

After $t = 30 ms$ current remains at $0 A$

So we can have the following graph:

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

67. II FIGURE P30.67 shows the potential difference across a potential difference across a $50 mH$ inductor. The current through the inductor at $t = 0 s$ is $0.20 A$ . Draw a graph showing the current through the inductor from $t = 0 s$ to $t = 40 ms$

Short Answer

Step by step solution

Step 1. Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Fluids

Rotational Dynamics

Scientific Method Physics

Medical Physics

Radiation

Study anywhere. Anytime. Across all devices.

91影视

67. II FIGURE P30.67 shows the potential difference across a potential difference across a 50mHinductor. The current through the inductor at t=0sis 0.20A. Draw a graph showing the current through the inductor from t=0sto t=40ms

Short Answer

Step by step solution

Step 1. Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Fluids

Rotational Dynamics

Scientific Method Physics

Medical Physics

Radiation

Study anywhere. Anytime. Across all devices.

67. II FIGURE P30.67 shows the potential difference across a potential difference across a $50 mH$ inductor. The current through the inductor at $t = 0 s$ is $0.20 A$ . Draw a graph showing the current through the inductor from $t = 0 s$ to $t = 40 ms$