Kirchhoffs Laws II & Kirchhoffs Laws Examples Current law, KCL - PowerPoint PPT Presentation

2/3/20 Class Concepts • Open & short circuits • Series and parallel elements Kirchhoff’s Laws II & • Kirchhoff’s Laws Examples • Current law, KCL Equivalent Resistance • Voltage law, KVL • Equivalent resistance • Series R eq • Parallel R eq EGR 220, Chapter 2 February 4, 2020 2 Open Circuits: V & I Open Circuits: V & I 3 4 1

2/3/20 Homework Check-in Recap: Node, Branch, Series and || • A branch represents a single element such as a voltage source or a resistor. • A node is the point of connection between two or more branches. • Series elements share a node exclusively (no third element shares the node) • Parallel elements share the same two nodes 5 6 Kirchhoff’s Current Law Series, Parallel, Open & Short and other things you notice • Find i 1 , i 2 and i 3 • Label nodes • Write KCL eqn’s • Solve • We will use Ohm’s law when there are resistors in the circuit diagram 7 8 2

2/3/20 Kirchhoff’s Current Law Kirchhoff’s Current Law • From HW 1: Find i 1 , i 2 , i 3 and i 4 • Label nodes • Write KCL equation and solve (use Ohm’s law for actual resistor circuits) 9 10 Kirchhoff’s Voltage Law, KVL Ø Draw and label an electrical circuit that is consistent with the graph shown below. 25 20 Change in Potential 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Distance Around Circuit 11 3

2/3/20 25 Kirchhoff’s Voltage Law, KVL 20 Change in Potential • The conservation of _________ 15 10 • Combine Ohm’s law with KVL to 5 solve for ________? R 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Distance Around Circuit + R 2 v 2 – Kirchhoff’s Voltage Law • Apply KVL • Label voltages New Concept: • Write KVL eqn’s • We will solve later with mesh analysis Equivalent Resistance 15 16 4

2/3/20 Series Resistors Parallel Resistors • Find R eq (as a function of R 1 and R 2 ) • Find R eq (as a function of R 1 and R 2 ) I I total i total I 2 I 1 + + V 1 – + V 2 – V R 1 R 2 V s − 17 18 Ho How many minion ons can ge get through the do doorways? Doorways resist the flow of minions Larger doorway is <larger / smaller> resistance? 19 20 5

2/3/20 R = ? (low or high R?) What is the resistance to the flow of minions? R = ? (low or high R?) 21 22 Resistance = 1 piece Compare doorways above and below (Parallel Doorways) 23 24 6

2/3/20 Resistance = 2 pieces in series Resistance Increasing 25 26 Resistance Increasing More Equivalent Resistance • Combinations of series and parallel resistors • The same current flows through... • Series / parallel resistors? • (And the voltage across is divided) • The same voltage drop is across.. • Series / parallel resistors? • (Current through is divided) 27 28 7

2/3/20 Series & Parallel (text def) Equivalent Resistance – Draw … • Two or more elements are in series if • They exclusively share a single node and • Carry the same current. • Two or more elements are in parallel if • They are connected to the same two nodes and • Have the same voltage across them. R = AΩ R = ½A Ω R = 2A Ω 29 30 Identify Series and ||Elements, and Find R eq Identify Series and ||Elements, and Find R eq a a b b 31 32 8

2/3/20 Identify Series and ||Elements, and Find R eq 33 34 Equivalent Resistance Different R eq for Different Terminals • Equivalent resistance is terminal-dependent V drop a-b = I a-b *R eq % &'() *+, ! "# = - *+, • The ratio of voltage to current for specific terminals in a circuit 35 36 9

2/3/20 37 38 New Terminology • Series elements • Share one node exclusively • Carry the same current Questions? • Parallel elements • Share the same two nodes • Have the same voltage drop across • Equivalent resistance • The ratio of voltage to current for the terminals (nodes) of interest 39 10