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Engineering Fundamentals and Problem Solving, 6e Chapter 17 Electrical Circuits 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 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 2 Simple DC Electric Circuit and Symbols Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 3 Ohm’s Law Potential = Current X Resistance V IR Where V = Potential in volts R = Resistance in ohms I = Current in amperes Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 4 Resistors in Series V1 V2 V3 VT RT R1 R2 R3 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 5 Resistors in Parallel VT 1 1 1 1 RT R1 R2 R3 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 6 DC Electric Power P VI 2 V P R PI R 2 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 7 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.” Vdrops= 0 Kirchoff’s current law • “The algebraic sum of all of the currents coming into a node (junction) in a network must be zero.” Inode= 0 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 8 Circuit Example 17.7 Given the following circuit, determine the currents Ix, Iy, and Iz. Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 9 Circuit Example cont’d From Kirchhoff’s current law at point A Iy = Ix + Iz From Kirchhoff’s voltage law around left loop - Iy(2) + 14 – Ix(4) = 0 Around right loop - Iy(2) + 12 – Iz(6) = 0 Results in: Ix = 2A, Iy = 3A, Iz = 1A Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 10 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 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 11 Mesh Current Example Write the mesh current equations for this circuit. V1 V2 V1 – IaR1 – (Ia – Ib)R3 = 0 -V2 – (Ib – Ia)R3 – IaR2 = 0 Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 12
