Problem

A precision laboratory resistor is made of a coil…

09:33

Problem 62 Medium Difficulty

(a) Calculate the self-inductance of a 50.0 cm long, 10.0 cm diameter solenoid having 1000 loops. (b) How much energy is stored in this inductor when 20.0 A of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed 3.00 V?

Answer

a. $1.97 \times 10^{-2} \mathrm{H}$
b. 3$\cdot 94$
c. $13.13 \times 10^{-2} \mathrm{sec}$

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Physics 102 Electricity and Magnetism

College Physics for AP® Courses

Chapter 23

Electromagnetic Induction, AC Circuits, and Electrical Technologies

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Video Transcript

and it's probably we're going to talk about the conduct ins off a salon. Eso I say that we have a solemn noid that has n turns and a diameter de and a link fill. So the induct int l of the so annoyed is equal to mu zero. The vacuum permeability times in squared times the area of the cross section of the solenoid divided by out. Also, we need to know that, uh, the energy stored in, uh in in Dr is equal to the inductions times the current through the induct er squared, divided by two. And finally, that the electro motive force on an induct ER is equal to the indictments times the derivative of the current with respect to time. Okay, so, um, now in question A, we have to consider Sahl annoyed with 1000 turns the diameter of 10 centimeters and a length of 50 centimeters. And our goal is to calculate the induct INTs. So the intestines is mu zero. That's one point of 26 times 10 to the minus six Henry Promoter times in squared. That's 1000 squared times. Theo area. That's pi times. The radius of five centimeters squared divided by 0.5 m. So the length is it, which is 0.197 Henry, I'm sorry. This is not like this is the induct. Its sure for that. This is the importance in question. Be have to assume that the current through the solenoid is equal. Thio been in pairs and we have to calculate how much energy is stored. The energy is l I squared over two. So that's 0.197 Henry times 20 in pairs squared, divided by two. So you is equal to 3.94 joules. Okay, then in questions, see ah, way have that the maximum active motive force on the solid line must be three votes. And we want to know how much time it should take for the solenoid to completely, uh, discharge. That is for it to be turned off completely safe. So notice that the electro motive force is L D I the t. Um Actually, there should be a mind this year, sir, for that. Andi, I'm gonna write the i d. T. As now toe I divided by Delta t. So I'm gonna isolate out a t t. is equal to Mina's l don't I divided by the electro motive force, Understand, Delta I is the final value off Uh, the current That's I minus. I'm sorry. That zero minus I the initial so that the TSL I divided by absolute l zero point, uh 0197 Henry times the current off 20 in pairs divided by three votes so that a T is equal to 0.13 seconds. Notice that I put the minus sign there right here because Delta I is negative. Absolutely is given this positive. So I had to make up for that, but this is our answer.

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