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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
