1

Lecture 3:Resistive CircuitsNilsson & Riedel 3.1-3.4, 3.7

ENG17 (Sec. 2): Circuits I

Spring 2014

April 8, 2014

2

Overview

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

3

Series Connected Elements

• Resistors in series carry the same current– KCL proves this

• Resistors in series can be summed– KVL proves this

4

Overview

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

5

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

6

Overview

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

7

Voltage Divider

• One voltage supply, multiple voltage levels

8

Load

• RL = load = 1+ circuit elements that draw power from circuit– May alter voltage across parallel element

– But not if RL >> R2

9

Example

10

Overview

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

11

Current Divider

• One current supply, multiple current levels

12

Example

13

Overview

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

14

Voltage Division

• Generalization of voltage divider circuit

15

Current Division

• Generalization of current divider circuit

16

Example

17

Overview

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

18

Unable to get Req

• For example, Wheatstone bridge circuit (below) cannot be simplified with standard parallel/series rules

• Must use circuit transformation

19

Defining Delta/Pi and Y/T

Δ

Y T

π

20

Delta-to-Wye Circuit Transformation

• Equivalent resistance between nodes• Note: resistor values are NOT THE SAME

21

Apply to Wheatstone Bridge

22

Rear Window Defroster

23

Rear Window Defroster - Problem

• Need: Power dissipated per unit length is same in each conductor

24

Recap

• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits