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Assignment 12

# Assignment 12 - Class PEP112S2007 Assignment 12 Assignment...

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Class PEP112S2007 Assignment 12 Assignment is due at 11:00pm on Sunday, April 22, 2007 Credit for problems submitted late will decrease to 0% over the course of 10 hour(s) after the deadline has passed. The wrong answer penalty is 1% per part. Multiple choice questions are penalized as described in the online help. The unopened hint bonus is 1% per part. You are allowed 10 attempts per answer. The R-L Circuit: Responding to Changes Learning Goal: To understand the behavior of an inductor in a series R-L circuit. In a circuit containing only resistors, the basic (though not necessarily explicit) assumption is that the current reaches its steady-state value instantly. This is not the case for a circuit containing inductors. Due to a fundamental property of an inductor to mitigate any "externally imposed" change in current, the current in such a circuit changes gradually when a switch is closed or opened. Consider a series circuit containing a resistor of resistance and an inductor of inductance connected to a source of emf and negligible internal resistance. The wires (including the ones that make up the inductor) are also assumed to have negligible resistance.

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Let us start by analyzing the process that takes place after switch is closed (switch remains open). In our further analysis, lowercase letters will denote the instantaneous values of various quantities, whereas capital letters will denote the maximum values of the respective quantities. Note that at any time during the process, Kirchhoff's loop rule holds and is, indeed, helpful: . Part A Immediately after the switch is closed, what is the current in the circuit? Hint A.1 How to approach the problem Hint not displayed ANSWER: zero Part B Immediately after the switch is closed, what is the voltage across the resistor? Hint B.1 Ohm's law Hint not displayed ANSWER: zero
Part C Immediately after the switch is closed, what is the voltage across the inductor? Hint C.1 A formula for voltage across an inductor Hint not displayed ANSWER: zero Part D Shortly after the switch is closed, what is the direction of the current in the circuit? ANSWER: clockwise counterclockwise There is no current because the inductor does not allow the current to increase from its initial zero value. Part E Shortly after the switch is closed, what is the direction of the induced EMF in the inductor? ANSWER: clockwise counterclockwise There is no induced EMF because the initial value of the current is zero. The induced EMF does not oppose the current; it opposes the change in current. In this case, the current is directed counterclockwise and is increasing; in other words, the time derivative of the counterclockwise current is positive, which is why the induced EMF is directed clockwise. Part F

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Eventually, the process approaches a steady state. What is the current in the circuit in the steady state?
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