Download CSCI 2980: Introduction to Circuits, CAD, and Instrumentation

EENG 2610: Circuits Analysis
Class 3: Resistor Combinations, Wye-Delta
Transformations, Dependent Sources
Oluwayomi Adamo
Department of Electrical Engineering
College of Engineering, University of North Texas
Series and Parallel Resistor Combinations
Simplifying Resistor Combinations

To determine equivalent resistance at a pair of
terminals of a network


Begin at the end of the network opposite the terminals
Repeat the following two steps as needed to reduce the
network to a single resistor at the pair of terminals


Combine resistors in series
Combine resistors in parallel
Example 2.20: Determine resistance RAB
Resistor Specifications

Resistor Value


Tolerance


Standard resistor values are usually fixed, so to achieve a
specific value, we need to combine standard value resistors in a
certain configuration. (see Table 2.1 on page 45)
Typically, 5% and 10%, which specifies possible minimum and
maximum resistance values
Power Rating

Specifies the maximum power that can be dissipated by the
resistor. Typically, ¼ W, ½ W, 1 W, 2 W, …
p(t )  v(t )i (t )
v 2 (t )
 Ri (t ) 
R
2
Example 2.22: Find the range for both current and power dissipation
in the resistor if R has a tolerance of 10%.
2.7 k
Analyzing Circuits with Single Source
and Series-Parallel Combination of Resistors

Step 1


Step 2


Systematically reduce the resistive network so that the resistance
seen by the source is represented by a single resistor
Determine the source current for a voltage source or the source
voltage if a current source is present
Step 3

Expand the network, retracing the simplification steps, and apply
Ohm’s law, KVL, KCL, voltage division, and current division.
Example 2.24: Find all the currents and voltages labeled in the network
Wye-Delta Transformation
Can you simplify it?
Ra 
R1 R2
R1  R2  R3
R1 
Ra Rb  Rb Rc  Rc Ra
Rb
Rb 
R2 R3
R1  R2  R3
R2 
Ra Rb  Rb Rc  Rc Ra
Rc
Rc 
R3 R1
R1  R2  R3
R3 
Ra Rb  Rb Rc  Rc Ra
Ra
Y 
 Y
Ra  Rb 
R2 ( R1  R3 )
R1  R2  R3
R ( R  R2 )
Rb  Rc  3 1
R1  R2  R3
Rc  Ra 
Equivalent
Transform
R1 ( R2  R3 )
R1  R2  R3
For two networks to be equivalent at each corresponding pair of terminals,
it is necessary that the resistance at the corresponding terminals be equal.
Circuits with Dependent Sources


Controlled sources are used to model many important
physical devices
Problem Solving Strategy




When writing KVL and/or KCL equations for the network, treat the
dependent sources as though it were an independent source.
Write the equation that specifies the relationship of the dependent
source to the controlling parameter.
Solve the equations for the unknowns. Be sure that the number
of linearly independent equations matches the number of
unknowns.
Will see a lot of examples a little later.