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(a) Using the exact exponential treatment, find the time required for the current through a 2.00 $\mathrm{H}$ inductor in series with a 0.500$\Omega$ resistor to be reduced to 0.100$\%$ of its original value. (b) Compare your answer to the approximate treatment using integral numbers of $\tau$ (c) Discuss how significant the difference is.

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Physics 102 Electricity and Magnetism

Chapter 23

Electromagnetic Induction, AC Circuits, and Electrical Technologies

Electromagnetic Induction

Cornell University

Rutgers, The State University of New Jersey

University of Sheffield

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so here for party, we should first find the time constant of the R l circuit. This would be the inductive is divided by the resistance. So to Henry's divided by 0.5 arms and this is equaling four seconds And so we can say that the decay of the current I easy equal to the initial current times the exponential function of the negative time, divided by Tao, the time constant. And so we can say that this would be equaling 0.1 times the initial current initial current, of course, then cancels out and we have that the exponential function of negative T over four seconds would be equaling 0.1 and therefore time is gonna be equaling negative four seconds multiplied by the natural log of 40.1 and we find that towel is equaling 27.63 seconds. This would be the time taken to reduce to bring the current down 2.1% of its final of other if its initial current. So the final current is then 0.1% of its initial value in 27.63 seconds. And so now we can say that four part B. We can find the ratio between the time taken to the time Constant Tao. This would be 27 points. Six seconds. We can say rather recon say 2027.63 seconds divided by four seconds. And this is equaling 6.9 approximately. The next highest integer is gonna be seven. So we can simply say that the time is equaling seven times. So seven time Constance and so T is equaling 28 seconds, and we can then calculate the ratio. This would be your answer for part B and then sees calculate the ratio. This would be one minus 27.63 seconds, divided by 28 seconds, and this is equal in 280.132 So here, if the value of time is considered as an integer than about 1% of it, is inherent uncertainty in the given parameters and the new value of time is about 9% larger than the inherent uncertainty given the parameters. So this would be your answer for part C. That is the end of the solution. Thank you for

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