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

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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:

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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

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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

Physics of Motion

Thermodynamics

Famous Physicists

Physical Quantities And Units

Force

Nuclear Physics

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 $t = 40 ms$