ECE 201 Section 4 Lecture 4 Prof Peter Bermel January 18 2012 Notes on HW 1 Received 97 109 homeworks on time Mean score of 93 Standard deviation of 9 Don t panic about a low score Key comments Check legibility of your name consider including PUID Draw graphs neatly with both axes labeled 1 18 2012 ECE 201 4 Prof Bermel Definitions Node a connecting point between two or more circuit elements Branch part of a circuit one or more circuit elements with two terminals Gaussian surface enclosed surface where charge electromagnetic flux is calculated Parallel circuit two or more branches linked by two nodes Series circuit two or more branches linked by one node 1 18 2012 ECE 201 4 Prof Bermel Definitions Closed path series of connected nodes with the same beginning end Closed node sequence series of nodes where the same beginning end Connected circuit a circuit in which all nodes are connected to each other via a path of circuit elements 1 18 2012 ECE 201 4 Prof Bermel Kirchoff s Current Law Sum of all currents entering a node or Gaussian surface is zero at all times From the conservation of charge 0 for all t 0 for all t 0 for all t 1 18 2012 ECE 201 4 Prof Bermel Example 1 At node A input currents look like this I1 t2 I2 4t A I4 I3 4 What is the output current I4 1 18 2012 ECE 201 4 Prof Bermel Example 1 Solution At node A input currents look like this I1 t2 I2 4t A I4 I3 4 What is the output current I4 I4 t2 4t 4 t 2 2 1 18 2012 ECE 201 4 Prof Bermel Example 2 Given an ideal current source Io connected to 4 parallel resistors how is the current divided 10 2 5 6 3 Io What if 2 identical ICS s are connected in parallel In series What if only one has its current doubled 1 18 2012 ECE 201 4 Prof Bermel Example 2 Solution Given an ideal current source Io connected to 4 parallel resistors how is the current divided Io 10 10 Io 2 5 2 5 Io 6 6 Io 3 Io 3 Equal voltage drop across every resistor implies 1 1 18 2012 ECE 201 4 Prof Bermel Example 2 Solution Cont d 10 2 5 6 3 Io What if 2 identical ICS s are connected in parallel All currents in resistors double In series No change What if only one has its current doubled Currents triple in parallel unphysical in series 1 18 2012 ECE 201 4 Prof Bermel Kirchoff s Voltage Law Since voltage is a unique quantity at a given place and time see Lecture 2 Voltage drop between any two nodes is given by the difference of their voltages independent of path i e VAB VA VB It is directionally dependent e g VAB VBA since VA VB VB VA Sum of voltage drops over any closed loop is zero otherwise voltage would be non unique 1 18 2012 ECE 201 4 Prof Bermel Kirchoff s Voltage Law Alternative statements For connected circuits and any node sequence the voltage difference between the end points equals the sum of the voltage drops across each element e g VAD VAB VBC VCD since VAB VBC VCD VA VB VB VC VC VD VA VD For connected circuits the sum of node to node voltages over any closed node sequence is always zero a special case of the last rule 1 18 2012 ECE 201 4 Prof Bermel F 2 E Example 3 3 D 9 A 4 B 2 What are VDA VFD and VEC 1 18 2012 ECE 201 4 Prof Bermel C F 2 E Example 3 Solution 3 D 9 A 4 B 2 C What are VDA VFD and VEC VDA VDB VBA 9 V 4 V 13 V VFD VFE VED 2 V 3 V 5 V VEC VED VDB VBC 3 V 9 V 2 V 10 V 1 18 2012 ECE 201 4 Prof Bermel Homework HW 2 solution posting this morning HW 3 due today by 4 pm at EE 325B HW 4 due Friday DeCarlo Lin Chapter 2 Problem 3 Problem 6 Problem 14 see errata Fig P2 13 should be Fig P2 14 The first I1 4 A should be Iin 4 A Problem 17 1 18 2012 ECE 201 4 Prof Bermel
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