Ohm s Law, Kirchhoff s Law, Single loop circuits, Single node-pair circuits. Kevin D. Donohue, University of Kentucky 1

Transcription

1 Ohm s Law, Kirchhoff s Law, Single loop circuis, Single nodepair circuis Kevin D. Donohue, Universiy of Kenucky 1

2 The relaionship beween volage and curren hrough a maerial, characerized by resisance, is given by Ohm s Law: v ) R i ) Resisive elemens will always absorb power i.e. conver elecric energy o hea): i) + v) Kevin D. Donohue, Universiy of Kenucky 2

3 Resisance can be characerized in unis of ohms: R 1Ω 1V 1A Conducance can be characerized in unis of siemens: G 1S 1A 1V Kevin D. Donohue, Universiy of Kenucky 3

4 Find he volage across a 10Ω resisor when a curren of 4 A is passing hrough i. Find he curren in a.02s resisor when a volage drop of 10 V occurs across i. Find he resisance of an elemen ha exhibis a 14 V drop when 21 A pass hrough i. Kevin D. Donohue, Universiy of Kenucky 4

5 Kevin D. Donohue, Universiy of Kenucky 5 Power absorbed by a resisor is given by: + v) i) G ) )R ) )R )G R ) R ) ) ) ) ) ) i i i i p) v v v v p i v p R + v) i) G

6 If a resisance value goes o infiniy, no curren flows hrough i. This is referred o as an open circui. + Lim + i) R v) i) R v) If a resisance value goes o zero, no volage drops across i. This is referred o as a shor circui. + Lim + i) R v) i) R 0 v) Kevin D. Donohue, Universiy of Kenucky 6

7 Solve for quaniies volage, power, curren, resisance) in resisive circuis wih simple connecions o independen and dependen sources. Kevin D. Donohue, Universiy of Kenucky 7

8 To represen he flow of elecrical charge hrough an acual circui, a zeroresisance connecor is used o connec symbols denoing elecrical properies of circui pars. Kevin D. Donohue, Universiy of Kenucky 8

9 Define and Idenify Nodes, Branches, Loops R1 1K R3 1K R2 1K I R0 1K R 1K V Node connecion beween 2 or more circui elemens Branch circui porion conaining a single elemen Loop closed pah conaining no node more han once Kevin D. Donohue, Universiy of Kenucky 9

10 The sum of all currens enering a node or any closed surface) equals zero Label each branch curren and wrie a se of equaions based on KCL Draw an arbirary surface conaining several nodes and wrie an equaion based on KCL R1 1K R3 1K R2 1K I R0 1K R 1K V Kevin D. Donohue, Universiy of Kenucky 10

11 Sum of all currens leaving a node equals zero. Denoe leaving as posiive and enering as negaive. Sum of all currens enering a node equals zero. Denoe enering as posiive and leaving as negaive. Sum of all currens leaving a node equals sum of all curren enering he node. Place all currens enering a node on one side of equaion and all currens leaving he node on he oher side. Kevin D. Donohue, Universiy of Kenucky 11

12 For circuis conaining independen sources, dependen sources, and resisors, use KCL and Ohm s Law o solve for unknown currens and volages OR deermine relaions beween quaniies ha canno be resolved i.e when more unknowns han independen equaions exis). Kevin D. Donohue, Universiy of Kenucky 12

13 The sum of all volages around any loop equals zero Label each branch volage and wrie a se of equaions based on KVL R1 1K R3 1K R2 1K I R0 1K R 1K V Kevin D. Donohue, Universiy of Kenucky 13

14 Sum of all volage drops around a loop equals zero. Denoe drops as posiive and rises as negaive. Sum of all volage rises around a loop equals zero. Denoe rises as posiive and drops as negaive. Sum of all volage rises equals he sum of all volage drops around a loop. Place all volage rises on one side of equaion and all volage drops on he oher side. Kevin D. Donohue, Universiy of Kenucky 14

15 V R0 V ab V ba a R0 b V V ac V ca V + V R0 + c V R R V o V o V R V bc V cb Kevin D. Donohue, Universiy of Kenucky 15

16 For circuis conaining independen sources, dependen sources, and resisors, use KVL o solve for unknown volages and currens or deermine relaion beween quaniies ha canno be resolved i.e. when more unknowns han independen equaions exis). Kevin D. Donohue, Universiy of Kenucky 16

17 Solving for circui quaniies will involve he following seps: Labeling he circui Deriving a se of equaion from circui Solving he resuling equaions Kevin D. Donohue, Universiy of Kenucky 17

18 Find reduced expressions for all unknown volages and currens V1 5v, V22v, R13kΩ, R22kΩ, R35kΩ): R1 V2 R2 V1 I R3 Hin: Curren in a single loop is he same hrough all elemens, herefore use KVL. Kevin D. Donohue, Universiy of Kenucky 18

19 Find reduced expressions all unknown volages and currens I 1 1mA, R4kΩ): a V ab I 1 R A 1000 b Hin: Volage over a single node pair is he same over all elemens, herefore use KCL. Kevin D. Donohue, Universiy of Kenucky 19

20 For single loops wih resisive elemens and a volage source, he following formula can be used o compue he volage drop across any resisor: V s R 1 R 2 R N + V 1 + V 2 + V N V k V s R 1 + R 2 Rk + + R N Kevin D. Donohue, Universiy of Kenucky 20

21 For single node pairs wih resisive elemens and a curren source, he following formula can be used o compue he curren in any resisor: I 1 I 2 I N I s R 1 R 2 R 1 2 n N I k I s G Gk + G + + G Kevin D. Donohue, Universiy of Kenucky 21