EENG 2610: Circuits AnalysisClass 3: Resistor Combinations, Wye-Delta Transformations, Dependent Sources

Oluwayomi AdamoDepartment of Electrical EngineeringCollege 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

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)

Tolerance 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, …

R

tvtRi

titvtp

)()(

)()()(2

2

Example 2.22: Find the range for both current and power dissipation in the resistor if R has a tolerance of 10%.

k7.2

Analyzing Circuits with Single Source and Series-Parallel Combination of Resistors Step 1

Systematically reduce the resistive network so that the resistance seen by the source is represented by a single resistor

Step 2 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 TransformationCan you simplify it?

321

312 )(

RRR

RRRRR ba

321

213 )(

RRR

RRRRR cb

321

321 )(

RRR

RRRRR ac

Y

RRR

RRR

RRR

RRR

RRR

RRR

c

b

a

321

13

321

32

321

21

Y

R

RRRRRRR

R

RRRRRRR

R

RRRRRRR

a

accbba

c

accbba

b

accbba

3

2

1

For two networks to be equivalent at each corresponding pair of terminals, it is necessary that the resistance at the corresponding terminals be equal.

Equivalent Transform

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.