EE201 Lecture 4 P 1 Kirchoff s Current Law Kirchoff s Voltage Law Single Loop Node Circuits Terminology v1 iR Node common connection v2 point between two or more elements R1 Series circuit R2 iR node 1 vR Parallel circuit R1 R2 R3 i1 i2 i3 node 2 Branch a two terminal circuit element EE201 Lecture 4 P 2 Series circuits all two terminal elements must carry the same current Reason we assume circuits are composed of lumped elements Parallel circuits the same voltage drop appears across every circuit element node 1 vR R1 R2 i1 i2 R3 i3 node 2 node 1 vR R3 R1 i1 Representations of the same parallel circuit illustrating nodes of the circuit R2 i2 node 2 i3 EE201 Lecture 4 P 3 Kirchoff s Current Law KCL For lumped circuits the algebraic sum of the currents entering a node is zero for every instant of time Example Find the unknown current ix 3 A 4A 7A 3A ix 10 A 5A a ix 8A 12 A ix 7 A 4 A b ix EE201 Lecture 4 P 4 Solutions a 5 A b 4 A Implications of KCL 1 Current sources cannot be connected in series 2 A current source that delivers zero current is equivalent to an open circuit This source has infinite internal resistance vR vR I Io V Slope of I V curve is R 1 Therefore internal resistance of current source is infinite EE201 Lecture 4 P 5 Gaussian curves and surfaces A curve or surface that closes upon itself e g circle sphere ellipsoid KCL for a Gaussian curve or surface For lumped circuits the algebraic sum of the currents leaving or entering a Gaussian curve or surface is zero for all instants of time Example Find Ix 20 A 7 A Ix Solution Ix 13 A Gaussian curve EE201 Lecture 4 P 6 Closed path in a circuit A connection of twoterminal elements which begins and ends on the same node and only traverses each node in the connection one time Node voltage The voltage drop from a given node to a reference node The reference node is usually taken to be ground Denoted by a single subscript e g VA VB EE201 Lecture 4 P 7 Kirchoff s Voltage Law KVL Statement 1 For lumped circuits the algebraic sum of the voltage drops around any closed path is zero for every instant of time Statement 2 For lumped circuits and any pair of nodes j and k the voltage drop vjk from node j to node k is vjk vj vk at every instant of time where vj is the voltage at node j and vk is the voltage at node k both with respect to the reference node EE201 Lecture 4 P 8 Closed node sequence a finite sequence of nodes that begins and ends at the same node This is an extension of the closed path concept A B D C node E reference A B C D E A is a closed node sequence but not a closed path Kirchoff s Voltage Law KVL cont Statement 3 For lumped circuits and any node sequence A D B G P the voltage drop vAP vAD vDB vGP at every instant of time EE201 Lecture 4 P 9 Kirchoff s Voltage Law KVL cont Statement 4 For lumped circuits the algebraic sum of the node to node voltages for any closed node sequence is zero for every instant in time vAB Example Find vAB B A 5V D Solution From KVL 11 V C 9V vAB vBC vCD vDA 0 vAB 11 V 9 V 5 V 0 vAB 25 V EE201 Lecture 4 P 10 Implications of KVL 1 Voltage sources cannot be connected in parallel 2 A voltage source that supplies zero volts is equivalent to a short circuit This source has zero internal resistance v 0 vR I Vo V Slope of I V curve is R 1 Therefore internal resistance of ideal voltage source is zero EE201 Lecture 4 P 11 Example Find VAB and VBC if VB 36 V 2 C A B vx 18 10 40 V 2 vx node D Solution 1 vx vB 36 V 2 iC 72 A 3 vC R iC 10 x 72 A 720 V 4 Apply KVL VBC VB VC 36 V 720 V VBC 684 V 5 Apply KVL VAB 36 V 40 V 0 VAB 4 V EE201 Lecture 4 Example Find vx P 12 D 8V 6V v x 2 V A E C B 10 V 7V H G 5V 18 V F Solution Use KVL for closed path vx 2V 6V 8V 7V 18V 5V 10V 0 vx 14 V
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