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ECE 2100

Circuit Analysis

Lesson 5

Chapter 2

Series Resistors and Voltage Division

Parallel Resistors and Current Division

Daniel M. Litynski, Ph.D.

http://homepages.wmich.edu/~dlitynsk/

ECE 2100

Circuit Analysis

Lesson 4

Chapter 2

Kirchhoff’s

Current and Voltage Laws

ECE 2100

Circuit Analysis

Lesson 5

Chapter 2

Series Resistors and Voltage Division

Parallel Resistors and Current Division

4

2.4 Series Resistors and Voltage Division (1)

• Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.

• The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances.

• The voltage divider can be expressed as

N

n

nNeq RRRRR1

21

vRRR

Rv

N

n

n

21

Series Resistors and Voltage Division

• Principle of Voltage Division: For resistors in series, the source voltage v is divided among the resistors in direct proportion to their resistances.

• Voltage Divider: A circuit (or branch) consisting of resistors in series.

8

Example 3

10V and 5

are in

series

2.4 Series Resistors and Voltage Division (1)

9

2.5 Parallel Resistors and Current Division (1)

• Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

• The equivalent resistance of a circuit with N resistors in parallel is:

• The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:

Neq RRRR

1111

21

n

eq

n

nR

iR

R

vi

Parallel Resistors and Current Division

• The equivalent conductance of resistors connected in parallel is the sum of their individual conductances.

• Principle of Current Division: For resistors in parallel, the total current i is shared by the resistors in inverse proportions to their resistances. Note Larger current flows through the smaller resistance.

• Current Divider: A circuit (or branch) consisting of resistors in parallel

13

Example 4

2 , 3 and 2A

are in parallel

2.5 Parallel Resistors and Current Division (1)

31

2.6 Wye-Delta Transformations

)(1

cba

cb

RRR

RRR

)(2

cba

ac

RRR

RRR

)(3

cba

ba

RRR

RRR

1

133221

R

RRRRRRRa

2

133221

R

RRRRRRRb

3

133221

R

RRRRRRRc

Delta -> Star Star -> Delta