ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Lecture 3:
Resistive Circuits
Nilsson & Riedel 3.1-3.4, 3.7
ENG17 (Sec. 2): Circuits I
Spring 2014
April 8, 2014
1
Overview
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
2
Copyright 2014.
All Rights Reserved.
1
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Series Connected Elements
• Resistors in series carry the same current
– KCL proves this
• Resistors in series can be summed
– KVL proves this
3
Overview
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
4
Copyright 2014.
All Rights Reserved.
2
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Parallel Connected Elements
• Resistors in parallel have same voltage
across their terminals
– KVL proves this
• Resistors in parallel can be summed
inversely
– KCL proves this
– Conductances are summed
5
Overview
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
6
Copyright 2014.
All Rights Reserved.
3
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Voltage Divider
• One voltage supply, multiple voltage levels
7
Load
• RL = load = 1+ circuit elements that draw
power from circuit
– May alter voltage across parallel element
– But not if RL >> R2
8
Copyright 2014.
All Rights Reserved.
4
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Example
9
Overview
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
10
Copyright 2014.
All Rights Reserved.
5
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Current Divider
• One current supply, multiple current levels
11
Example
12
Copyright 2014.
All Rights Reserved.
6
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Overview
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
13
Voltage Division
• Generalization of voltage divider circuit
14
Copyright 2014.
All Rights Reserved.
7
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Current Division
• Generalization of current divider circuit
15
Example
16
Copyright 2014.
All Rights Reserved.
8
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Overview
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
17
Unable to get Req
• For example, Wheatstone bridge circuit
(below) cannot be simplified with standard
parallel/series rules
• Must use circuit transformation
18
Copyright 2014.
All Rights Reserved.
9
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Defining Delta/Pi and Y/T
∆
π
Y
T
19
Delta-to-Wye Circuit Transformation
• Equivalent resistance between nodes
• Note: resistor values are NOT THE SAME
20
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All Rights Reserved.
10
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Apply to Wheatstone Bridge
21
Rear Window Defroster
22
Copyright 2014.
All Rights Reserved.
11
ENG 17: Circuits I (Spring 2014, UC Davis)
Instructor: Dr. Montgomery
Rear Window Defroster - Problem
• Need: Power dissipated per unit length is
same in each conductor
23
Recap
•
•
•
•
•
Resistors in Series
Resistors in Parallel
Voltage Divider
Current Divider
Voltage / Current
Division
• ∆-to-Y Equivalent
Circuits
24
Copyright 2014.
All Rights Reserved.
12