Engineering Fundamentals and Problem Solving, 6e Chapter 17 Electrical Circuits

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Objectives Compute the equivalent resistance of resistors in series and in parallel Apply Ohm’s law to a resistive circuit Determine the power provided to a DC circuit and the power used by circuit components Use Kirchhoff’s laws to solve resistive networks Utilize mesh currents to solve resistive networks 2

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Simple DC Electric Circuit and Symbols 3

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Ohm’s Law Potential = Current X Resistance Where V = Potential in volts R = Resistance in ohms I = Current in amperes 4

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Resistors in Series 5 V1V1 V2V2 V3V3 VTVT

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Resistors in Parallel 6 VTVT

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. DC Electric Power 7

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Kirchhoff’s Laws Kirchoff’s voltage law “The algebraic sum of all the voltages (potential drops) around any closed loop in a network equals zero.”  V drops = 0 Kirchoff’s current law “The algebraic sum of all of the currents coming into a node (junction) in a network must be zero.”  I node = 0 8

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Circuit Example 17.7 Given the following circuit, determine the currents I x, I y, and I z. 9

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Circuit Example cont’d From Kirchhoff’s current law at point A I y = I x + I z From Kirchhoff’s voltage law around left loop - I y (2) + 14 – I x (4) = 0 Around right loop - I y (2) + 12 – I z (6) = 0 Results in: I x = 2A, I y = 3A, I z = 1A 10

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Mesh Currents A node is a specific point or location within a circuit where two or more components are connected. A branch is a path that connects two nodes. A mesh is a loop that does not contain any other loops within itself. Mesh currents  Exist only in the perimeter of the mesh  Selected clockwise for each mesh  Travel all the way around the mesh 11

Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Mesh Current Example Write the mesh current equations for this circuit. V 1 – I a R 1 – (I a – I b )R 3 = 0 -V 2 – (I b – I a )R 3 – I a R 2 = 0 12 V1V1 V2V2