1. Copyright © 2009 Pearson Education, Inc. Admin: Assignment 8 is complete Assignment 9 is posted 2 more AC analysis problems RC circuits Due Monday (May 4 th ) Second mid-term date is Wednesday May 6 th

2. Copyright © 2009 Pearson Education, Inc. A circuit consisting of an inductor and a resistor will begin with most of the voltage drop across the inductor, as the current is changing rapidly (t=0). With time, the current will increase less and less, until all the voltage is across the resistor (t=∞). 30-4 LR Circuits We talk about "Charging” a capacitor, "Current build-up” or “energizing” an inductor

3. Time response of Inductors Switch to position a: Integrate and apply boundary condition t=0, i=0 Time constant τ=L/R. Talk about "Charging a capacitor" "Current build-up" in an inductor

4. Copyright © 2009 Pearson Education, Inc. If the circuit is then shorted across the battery, the current will gradually decay away: 30-4 LR Circuits. Switch to position b:

5. Copyright © 2009 Pearson Education, Inc. 30-4 LR Circuits Example 30-6: An LR circuit. At t = 0, a 12.0-V battery is connected in series with a 220-mH inductor and a total of 30-Ω resistance, as shown. (a) What is the current at t = 0? (b) What is the time constant? (c) What is the maximum current? (d) How long will it take the current to reach half its maximum possible value?.

6. Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations An LC circuit is a charged capacitor shorted through an inductor.

7. Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations Summing the potential drops around the circuit gives a differential equation for Q : This is the equation for simple harmonic motion, and has solutions.. The charge on the capacitor oscillates!

8. Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations Substituting shows that the equation can only be true for all times if the frequency is given by The current in the inductor also oscillates:

9. Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations The charge and current both oscillate, but with different phases..