Problem Set 9


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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Problem Set 9 Due: Wednesday, April 16 at 11 am. Hand in your problem set in your section slot in the boxes outside the door of 32- 082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3 Group A) Problem 1: Read Experiment 6: Inductance and RL Circuits Pre-Lab Questions (10 points) 1. RL Circuits (3 points) Consider the circuit at left, consisting of a battery (emf ε ), an inductor L , resistor R and switch S . For times t < 0 the switch is open and there is no current in the circuit. At t = 0 the switch is closed. (a) Using Kirchhoff’s loop rules (really Faraday’s law now), write a differential equation relating the emf on the battery, the current in the circuit and the time derivative of the current in the circuit. (b) The solution to your differential equation should look: / () ( ) t It AX e τ =− where A , X , and are constants. Plug this expression into the differential equation you obtained in (a) in order to confirm that it indeed is a solution and to determine what the time constant and the constants A , and X are. What would be a better label for A ? (HINT: You will also need to use the initial condition for current. What is (0 ) = ?) (c) Now that you know the time dependence for the current I in the circuit you can also determine the voltage drop V R across resistor and the EMF generated by the inductor. Do so, and confirm that your expressions match the plots in Fig. 6a or 6b in Experiment 6.
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2. ‘Discharging’ an Inductor (3 points) After a long time T the current will reach an equilibrium value and inductor will be “fully charged.” At this point we turn off the battery ( ε =0), allowing the inductor to ‘discharge,’ as pictured at left. Repeat each of the steps a-c in problem 1, noting that instead of exp(- t / τ ), our expression for current will now contain exp(-( t - T )/ ). 3. A Real Inductor (2 points) As mentioned above, in this lab you will work with a coil that does not behave as an ideal inductor, but rather as an ideal inductor in series with a resistor. For this reason you have
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This note was uploaded on 11/10/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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