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 $Δ V_{L}$ across the inductor for these $6 ms$ .

Short Answer

Expert verified

The potential difference across the inductor is

$\begin{array}{l} Δ V_{L} = - 10 Vfor 0 ms < t < 2 ms \\ Δ V_{L} = 0 V for 2 ms < t < 3 ms \\ Δ V_{L} = 20 V for 3 ms < t < 5 ms \\ Δ V_{L} = 0 V for t > 5 ms \end{array}$

Step by step solution

Step 1. Introduction

It is given that the value of inductor, $L = 10 mH = 10 \times 10^{- 3} H$

We have potential difference across the inductor as $Δ V_{L} = - L \frac{d I}{d t}$

Step 2. Explanation

From $t = 0 ms$ to $t = 2 ms$ , current $I$ changes from $0 A to 2A$ .

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

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 $- 2 A$

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

So, the inductor voltage is

$Δ V_{L} = 1 (10 \times 10^{- 3} H) (- 2000 A / s) = 20 V$

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66. II FIGURE P30.66 shows the current through a $10 mH$ inductor. Draw a graph showing the potential difference $Δ V_{L}$ 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.

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66. II FIGURE P30.66 shows the current through a10mH inductor. Draw a graph showing the potential differenceΔVL 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

Electricity and Magnetism

Electrostatics

Mechanics and Materials

Medical Physics

Measurements

Astrophysics

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 $Δ V_{L}$ across the inductor for these $6 ms$ .