ECE 201 Section 4 Lecture 14 Prof Peter Bermel February 13 2012 Returning Homeworks HW 10 N 95 82 22 2 13 2012 ECE 201 4 Prof Bermel Exam 1 Thursday Feb 9 Will post copy of the exam on Blackboard Will return scores ASAP 2 13 2012 ECE 201 4 Prof Bermel Inductors Inductors resist changes in the flow of current Physically derived from Ampere s law a flowing current creates a constant magnetic field Faraday s law a changing magnetic field induces an emf Mathematically 2 13 2012 ECE 201 4 Prof Bermel Example 1 With a wall AC voltage source of 160 sin 120 turned on at t 0 with an inductor L 40 H what is the current as a function of time for this circuit 160 sin 120 t 2 13 2012 ECE 201 4 Prof Bermel 40 H Example 1 Solution 160 sin 120 t 40 H With the inductor 0 160 sin 120 40 4 sin 120 1 1 cos 120 30 2 13 2012 ECE 201 4 Prof Bermel Calculating Inductance General formula for inductance 4 For solenoid where magnetic constant usu o 4 x10 7 H m N number of loops A cross sectional area of solenoid l length of solenoid 2 13 2012 ECE 201 4 Prof Bermel Deriving Inductance Faraday s law states From the definitions for L and A From Amp re s law 4 2 13 2012 ECE 201 4 Prof Bermel Combining Inductors Define In series 0 0 Alternative proof 0 0 By KCL 0 and 0 so 0 2 13 2012 ECE 201 4 Prof Bermel Combining Inductors In parallel 0 0 Conservation of current 0 implies 0 0 2 13 2012 ECE 201 4 Prof Bermel Combining Inductors Assuming is non zero 0 1 0 0 1 0 1 0 0 0 2 13 2012 ECE 201 4 Prof Bermel Combining Inductors We can use induction to prove the following Combining inductors in series 4 2 3 350 Combining inductors in parallel 4 1 1 2 3 350 2 13 2012 ECE 201 4 Prof Bermel Example 2 What is the equivalent inductance current division and power dissipated between the 2 branches of this circuit 15 H 20 7 8 2 13 2012 30 H ECE 201 4 Prof Bermel 45 H Example 2 Solution 15 H 20 7 8 30 H 80 0 0 9 0 45 H 20 H 30 0 20 0 2 3 1 3 2 13 2012 ECE 201 4 Prof Bermel Example 2 Solution 15 H 20 7 8 2 13 2012 30 H 45 H 20 7 8 7 8 1 A s 0 30 0 60 20 400 7 8 1 ECE 201 4 Prof Bermel Homework HW 12 solution posted today HW 13 due today by 4 pm in EE 326B HW 14 due Mon DeCarlo Lin Chapter 6 Problem 48 Problem 53 check left hand side of circuit has an independent current source is1 pointing upwards 2 13 2012 ECE 201 4 Prof Bermel
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