Transcript Engineering Fundamentals and Problem Solving, 6e

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.
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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.
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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.
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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.
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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.
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DC Electric Power
P  VI
2
V
P
R
PI R
2
Engineering: Fundamentals and Problem Solving, 6e
Eide  Jenison  Northup  Mickelson
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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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.
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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.
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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.
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