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The "square-wave" voltage shown in Figure $24-31$ is applied to an $R L$ circuit. Sketch the shape of the instantaneous voltage across the inductor, assuming the time constantof the circuit is much less than the period of the applied voltage.

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Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

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essentially, we're going. Thio essentially saw for the induced Ian mess for the three different periods of time. So we can say that the magnitude of the induced in math would be equal to the absolute value of the induced enough. This would equal the induct INTs, times the absolute value of the change in the current, divided by the change in time. So essentially for part A, we have zero 22 milliseconds. Eso essentially our induced e m F up salon would be equal to the induct INTs l so for 0.6 Henry's and then multiplied by the absolute value of a 7.0 amps minus zero, divided by 2.0 times 10 to the negative third seconds. And we find that the induced in F would be 1.6 times 10 to the fourth bolts. Now, for Part B, we can say from two milliseconds to five milliseconds. The induced, the absolute. The magnitude of the induced E. M f uh would be equal to here. It would be again 4.6 Henry's and then the absolute value of 5.0 amps, minus 7.0 amps. Again, this is a going to produce a negative value. So this is just one example of why we need to use the absolute value bars. This would be divided by five minus two times 10 to be negative third seconds. And we find Kathy induced in meth for this time interval 3.1 times 10 to the third revolts. So this would be our answer for part b r answer for part A and for finally for court. See, we're evaluating five milliseconds to six minutes seconds. And so we can say that the induced the magnitude of the induced IMF would be equal to again the deduct the induct in CE of 4.6 Henry's times the absolute value of zero minus 5.0 amps. So this is another example of where the absolute value bars create a creative positive results rather than a negative result, and then six minus 51 So it would be one times 10 to the negative 3rd 2nd so again, milliseconds. And this is equaling 2.3 times 10 to the fourth bolts. This would be our induced IMF for part C. That is the end of the solution. Thank you for watching

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