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

V

1

V

2

V

3

V

T

R T



R

1 

R

2 

R

3 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

V

T 1

R T

 1

R

1  1

R

2  1

R

3 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 P



V

2

R P



I

2

R

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.” 

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

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

I x , I y

, and I

z.

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

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 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.

V

1

V

1

-V

2 – I

a R

1 – (I

b

– (I

a – I b

)R 3

– I a

)R 3 – I

a R

2 = 0 = 0 Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

V

2 12