# UK EE 211 - Circuit Laws (21 pages)

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## Circuit Laws

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- Pages:
- 21
- School:
- University of Kentucky
- Course:
- Ee 211 - Circuits I

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Circuit Laws Ohm s Law Kirchhoff s Law Single loop circuits Single node pair circuits Kevin D Donohue University of Kentucky 1 Ohm s Law The relationship between voltage and current through a material characterized by resistance is given by Ohm s Law v t R i t Resistive elements will always absorb power i e convert electric energy to heat Kevin D Donohue University of Kentucky i t v t 2 Units for Resistance Conductance Resistance can be characterized in units of ohms 1V R 1 1A Conductance can be characterized in units of siemens 1A G 1S 1V Kevin D Donohue University of Kentucky 3 Examples Find the voltage across a 10 resistor when a current of 4 A is passing through it Find the current in a 02S resistor when a voltage drop of 10 V occurs across it Find the resistance of an element that exhibits a 14 V drop when 21 A pass through it Kevin D Donohue University of Kentucky 4 Power in a Resistive Element Power absorbed by a resistor is given by i t R p t v t i t v t v 2 t 2 p t v t v t G R R 2 i t 2 p t i t Ri t i t R G Kevin D Donohue University of Kentucky i t G v t v t 5 Open and Short Circuits If a resistance value goes to infinity no current flows through it This is referred to as an open circuit Lim i t i t v t R v t R If a resistance value goes to zero no voltage drops across it This is referred to as a short circuit Lim i t i t v t R v t R 0 Kevin D Donohue University of Kentucky 6 Examples Solve for quantities voltage power current resistance in resistive circuits with simple connections to independent and dependent sources Kevin D Donohue University of Kentucky 7 Lumped Parameter Circuit To represent the flow of electrical charge through an actual circuit a zeroresistance connector is used to connect symbols denoting electrical properties of circuit parts Kevin D Donohue University of Kentucky 8 Lumped Parameter Circuit Define and Identify Nodes Branches Loops R1 1K R2 1K R3 1K R0 1K R 1K V I Node connection between 2 or more circuit elements Branch circuit portion containing a single element Loop closed path containing no node more than once Kevin D Donohue University of Kentucky 9 Kirchhoff s Current Law KCL The sum of all currents entering a node or any closed surface equals zero Label each branch current and write a set of equations based on KCL Draw an arbitrary surface containing several nodes and write an equation based on KCL R1 1K R2 1K R3 1K R0 1K R 1K V I Kevin D Donohue University of Kentucky 10 KCL Statements and Sign Sum of all currents leaving a node equals zero Denote leaving as positive and entering as negative Sum of all currents entering a node equals zero Denote entering as positive and leaving as negative Sum of all currents leaving a node equals sum of all current entering the node Place all currents entering a node on one side of equation and all currents leaving the node on the other side Kevin D Donohue University of Kentucky 11 Examples For circuits containing independent sources dependent sources and resistors use KCL and Ohm s Law to solve for unknown currents and voltages OR determine relations between quantities that cannot be resolved i e when more unknowns than independent equations exist Kevin D Donohue University of Kentucky 12 Kirchhoff s Voltage Law KVL The sum of all voltages around any loop equals zero Label each branch voltage and write a set of equations based on KVL R1 1K R2 1K R3 1K R0 1K R 1K V I Kevin D Donohue University of Kentucky 13 KVL Statements and Sign Sum of all voltage drops around a loop equals zero Denote drops as positive and rises as negative Sum of all voltage rises around a loop equals zero Denote rises as positive and drops as negative Sum of all voltage rises equals the sum of all voltage drops around a loop Place all voltage rises on one side of equation and all voltage drops on the other side Kevin D Donohue University of Kentucky 14 Voltage Labeling VR 0 Vab Vba a b VR0 R V R0 V Vac Vca VR Vo Vo VR Vbc Vcb c Kevin D Donohue University of Kentucky 15 Examples For circuits containing independent sources dependent sources and resistors use KVL to solve for unknown voltages and currents or determine relation between quantities that cannot be resolved i e when more unknowns than independent equations exist Kevin D Donohue University of Kentucky 16 Single Loop and Node Circuits Solving for circuit quantities will involve the following steps Labeling the circuit Deriving a set of equation from circuit Solving the resulting equations Kevin D Donohue University of Kentucky 17 Single Loop Example Find reduced expressions for all unknown voltages and currents V1 5v V2 2v R1 3k R2 2k R3 5k R1 V2 V1 R2 I R3 Hint Current in a single loop is the same through all elements therefore use KVL Kevin D Donohue University of Kentucky 18 Single Node Pair Example Find reduced expressions all unknown voltages and currents I1 1mA R 4k a I1 Vab A 1000 R b Hint Voltage over a single node pair is the same over all elements therefore use KCL Kevin D Donohue University of Kentucky 19 Voltage Division For single loops with resistive elements and a voltage source the following formula can be used to compute the voltage drop across any resistor R1 Vs R2 V1 V2 RN Rk Vk Vs R1 R2 RN VN Kevin D Donohue University of Kentucky 20 Current Division For single node pairs with resistive elements and a current source the following formula can be used to compute the current in any resistor I1 Is R1 R2 I2 IN RN Gk I k I s G1 G2 Gn Kevin D Donohue University of Kentucky 21

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