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PRESENT everything you know about the problem.
To find equivalent resistance, the resistor network must be reduced using series
combinations, parallel combinations, and conversions between wye and delta connected
resistors. We know that series resistances are added to obtain the equivalent resistance and
the inverse of parallel resistances are added to obtain the inverse of the equivalent resistance;
i.e.
R eq = R 1 + R 2
1 R eq = 1 R 1 + 1 R 2
and
We also know how to convert between wye and delta connected loads, as seen previously in
this section.
Establish a set of ALTERNATIVE solutions and determine the one that promises the
greatest likelihood of success.
The set of alternatives to reducing resistor networks involves the various ways that resistors
can be combined. In this case, we will convert the lower ∆ connection to a Y connection.
Then, we will combine parallel resistors (two series resistors are in parallel with two series
resistors) to get a series combination. This will produce the equivalent resistance of the
resistor network.
ATTEMPT a problem solution. 10 Ω
2Ω
4Ω Req v v 5Ω   14 Ω eText Main Menu 8Ω  Textbook Table of Contents  R a + R b + R c = 8 + 5 + 4 = 17
(4)(5)
R1 =
= 1.1765
17
(4)(8)
R2 =
= 1.8824
17
(5)(8)
R3 =
= 2.353
17 Problem Solving Workbook Contents 10 Ω
2Ω 14 Ω 2 + 1.1765 = 3.177
14 + 1.8824 = 15.882 Req 3.177 15.882
1.1765 Ω 1.8824 Ω (3.177)(15.882)
3.177 + 15.882
50.46
=
= 2.647
19.059
= 2.353 Ω 10 Ω 2.647 Ω Req 10 + 2.647 + 2.353 = 15 2.353 Ω Req Therefore, R eq = 15 ohms. 15 Ω EVALUATE the solution and check for accuracy.
To check for accuracy, reduce the resistor network by converting the upper ∆ connection to a
Y connection. Then, combine parallel resistors (two series resistors are in parallel with two
series resistors) to get a series combination. This will produce the equivalent resistance of the
resistor network.
It can be shown that 10 Ω
2Ω
4Ω Req v v 5Ω   eText Main Menu 14 Ω 8Ω  Textbook Table of...
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 Spring '12
 bkav

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