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

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=∞) LR Circuits We talk about "Charging” a capacitor, "Current build-up” or “energizing” an inductor

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

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:

Copyright © 2009 Pearson Education, Inc 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?.

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

Copyright © 2009 Pearson Education, Inc 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!

Copyright © 2009 Pearson Education, Inc 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:

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