Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12EE201 Lecture 4 P. 1Kirchoff’s Current Law, Kirchoff’s Voltage Law, Single Loop/Node CircuitsTerminologyR1R2iR__++iRv2v1Node: common connectionpoint between two or more elements.Series circuit vRR1R2R3_+Parallel circuitnode 1node 2i1i2i3Branch - a two-terminal circuit element.EE201 Lecture 4 P. 2Series 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. vRR1R2R3_+node 1node 2i1i2i3 vRR1R2R3_+i1i2i3node 2node 1Representations of the same parallel circuit illustrating nodes of the circuit.EE201 Lecture 4 P. 3Kirchoff’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.4 A7 A3 A10 A5 Aix-3 A8 A12 A-7 A-4 Aix(a) ix = (b) ix =EE201 Lecture 4 P. 4Solutions: (a) 5 A, (b) -4 AImplications 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_+IoIVSlope of I-V curve is R-1. Therefore, internal resistance of current source is infinite.EE201 Lecture 4 P. 5Gaussian curves and surfacesA 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.Gaussian curve20 A-7 AIxSolution: Ix = -13 A.EE201 Lecture 4 P. 6Closed path in a circuit: A connection of two-terminal 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. 7Kirchoff’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 - vkat 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. 8Closed node sequence: a finite sequence of nodes that begins and ends at the same node. This is an extension of the closed path concept. CBnode E (reference)DA+__+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. 9Kirchoff’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.Example: Find vAB.+_+_+_ABCD+5 V-11 VSolution: From KVL,vAB + vBC + vCD + vDA = 0vAB + (-11 V) + (-9 V) + (-5 V) = 0vAB = 25 V9 V_vABEE201 Lecture 4 P. 10Implications 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_+VoIVSlope of I-V curve is R-1. Therefore, internal resistance of ideal voltage source is zero.+_EE201 Lecture 4 P. 11CBA+_Example: Find VAB and VBC if VB = 36 V.40 V2 vx18 2 10 +_ vxSolution: 1) vx = vB = 36 V2) iC = 72 A3) vC = R iC = (10 ) x (72 A) = 720 V4) Apply KVL: VBC = VB - VC = 36 V - 720 V VBC = -684 V5) Apply KVL: VAB + 36 V - 40 V = 0 VAB = 4 V node DEE201 Lecture 4 P. 12Example: Find vx.10 Vvx+_+++++++_______2 V5 V18 V7 V8 V6 VSolution: Use KVL for closed path.vx + 2V - 6V + 8V + 7V + 18V - 5V - 10V = 0 vx = -14
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