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Your $R L$ circuit has a characteristic time constant of 20.0 ns, and a resistance of 5.00 $\mathrm{M\Omega}$ . (a) What is the inductance of the circuit? (b) What resistance would give you a 1.00 ns time constant, perhaps needed for quick response in an oscilloscope?

$1 \times 10^{8} \Omega$

Physics 102 Electricity and Magnetism

Chapter 23

Electromagnetic Induction, AC Circuits, and Electrical Technologies

Electromagnetic Induction

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so here for part A. We know that the time Constant Tao is equaling the induct INTs over the resistance for an R L circuit, and so we can find that the induct in CE would simply be equals the product between the time constant and the resistance. The time constant here is 20 nanoseconds, so 20 times 10 to the negative ninth seconds multiplied by the resistance of five. Mega comes or five times 10 to the sixth homes, and we find that here, the induct Ince's equaling 0.10 Henry's we know for part B, this would be your answer for party for Part B. We know that the time Constant is again equaling the inductive over the resistance solving for the resistance. Now this would be equaling the inductive over the time constant, and here we're using the same induct its 0.10 Henry's. But now we're going to be dividing by one nanosecond. So one times 10 to the negative ninth second, and we find that our the resistance and Zen equaling 1.0 times 10 to the eighth Homes. This would be our final answer for Part B. That is the end of the solution. Thank you for watching

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