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PHYS270_HMWK3 - inductor 2 After the above-discussed steady...

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PHYS270 Homework #3 Due in recitation week of Feb. 21 An inductor of inductance L is placed in a circuit with a battery and two resistors as shown below. The switch has been held open for a long time. At t=0 the switch is closed and current begins to flow through resistor R 1 . 1. Without doing any analysis draw a schematic curve of the current as a function of time in resistor R 1 . You can determine the initial and final current based on the following points. A) Using the principle that that the current in the inductor cannot change instantaneously, and knowing its initial value, write a formula for the current in R 1 just after the switch closes. B) After a long time currents in the resistors and inductor will reach steady values. Knowing in that case what the voltage across the inductor must be, you can determine the values of the final, steady currents in the two resistors and the
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Unformatted text preview: inductor. 2. After the above-discussed steady state is reached, the switch is opened. What will be the voltage across the inductor just after the switch is opened? (Hint: much to the disappointment of many of you, there will be no sparks because R 2 is present.) 3. For the case when the switch has just been closed, label the currents in the three two-terminal elements I L , I 1 , I 2 . Write Kirchoff’s current law for the junction of R 1 , R 2 , and L. Write Kirchoff’s voltage law for the loop including the battery, R 1 and R 2 . Relate the voltage across the inductor to the voltage across R2. 4. (Bonus) Combine the above to write a single differential equation for the current in the inductor....
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