My Notes O Aak Your Teacher 49. -13 points SerCP10 20.P043. My Notes Ask Your An

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My Notes O Aak Your Teacher 49. -13 points SerCP10 20.P043. My Notes Ask Your An electromagnet can be modeled as an inductor in series with a resistor. Consider a large electromagnet of inductance L = 13.0 H and resistance R = 5.00 connected to a 12.0-V battery and switch as in the figure shown below. After the switch is closed, find the following. (a) the maximum current carried by the electromagnet (b) the time constant of the circuit (c) the time it takes the current to reach 95.0% of its maximum value Need Help? Read It Submit Assignment Save Assignment Progress Home My Assignments Extension Request WebAssign® 40 © 1997-2017 Advanced Instructonal Systems, Inc All rights reserved.

Explanation / Answer

a)The maximum current carried by the electromagnet will be given by:

I = V/R

I = 12/5 = 2.4 A

Hence, I = 2.4 A

b)We know that the time constant in an LR circuit is given by

time constant = tau = L/R = 13/5 = 2.6 s

Hence, time constant = 2.6 s

c)We know that the current at anytime t in the RL circuit is given by:

I = I(max) [1 - e^-tR/L]

I/I(max) = [1 - e^-tR/L]

0.95 = [1 - e^-tR/L]

e^-tR/L = 1 - 0.95 = 0.05

taking natural log both sides

-tR/L = -2.996

t = 2.996 x L/R = 2.996 x 13/5 = 7.79 s

Hence, t = 7.79 s

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