Question
Asked Aug 4, 2019
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The current i through a 5.3 H inductor varies with time t as shown by the graph of the figure. The inductor has a resistance of 9.9 Ω. Find the magnitude of the induced emf ε during the time intervals (a) t = 0 to 2 ms; (b) 2 ms to 5 ms, and (c) 5 ms to 6 ms. (Ignore the behavior at the ends of the intervals.)

 

6
34
4
6
2
(ms)
0
(v)!
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6 34 4 6 2 (ms) 0 (v)!

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Expert Answer

Step 1

Write the expression for the  induced emf in a inductor.

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here, i is the current, di tis the time Lis the inductance dt

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Step 2

Change in current for a given time can be determined from the graph.

(a)For time 0 to 2ms , the change in current is 0 to 7 A.

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substitute, 5.3 H for L di E = -L dt 7A for i, 2 x103s for t 7A =(5.3H) 2x103 =-1.85x 104 V

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Step 3

(b) For time 2 ms to 5ms  , the c...

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substitute, 5.3 H for L di 7-3 dt 5A 7A for i, 3x103s for t (5A 7A — -(5.ЗН) 3x10 S =3.53x 103 v

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Science

Physics

Electromagnetic Induction

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