Chapter 30: Q46P (page 899)

The current i through a 4.6 Hinductor varies with time t as shown by the graph of Figure, where the vertical axis scale is set by $i_{s} = 8.0 A$ and the horizontal axis scale is set by $t_{s} = 6.0 m s$ . The inductor has a resistance of $12 Ω$ .(a) Find the magnitude of the induced emf $ε$ during time intervals 0 to 2 ms. (b) Find the magnitude of the induced emf $ε$ during time intervals 2 ms to 5 ms. (c) Find the magnitude of the induced emf $ε$ during time intervals 5 ms to 6 ms. (Ignore the behavior at the ends of the intervals.)

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Step by step solution

$i_{s} = 8 A t_{s} = 6 m s$

According to Faraday’s law, the emf induced in a circuit is proportional to the time rate of change of the magnetic flux linking that circuit.

Formulae:

Induced emfis given by

$ε = L \frac{d i}{d t}$

Induced emf $ε$ is given by

$\overset{,}{o} = L \frac{d i}{d t} i = 0 t o 7 A ε = L \frac{d i}{d t} = \frac{4.6 \times (7 - 0)}{(2 - 0) \times 10^{- 3}} ε = 1.6 \times 10^{4} V$

For time interval 2ms to 5ms

$1 = 7 t 0 5 A ε = L \frac{d i}{d t} = \frac{4.6 \times (5 - 7)}{(5 - 2) \times 10^{- 3}} ε = 3.1 \times 10^{3} V$

For time interval 5ms to 6ms

$1 = 0 t o 5 A ε = L \frac{d i}{d t} = \frac{4.6 \times (5 - 0)}{(6 - 5) \times 10^{- 3}} ε = 2.3 \times 10^{4} V$

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