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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;
R eq = R 1 + R 2
1 R eq = 1 R 1 + 1 R 2
We also know how to convert between wye and delta connected loads, as seen previously in
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
ATTEMPT a problem solution. 10 Ω
4Ω Req v v 5Ω | | 14 Ω e-Text Main Menu 8Ω | Textbook Table of Contents | R a + R b + R c = 8 + 5 + 4 = 17
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
= 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
It can be shown that 10 Ω
4Ω Req v v 5Ω | | e-Text Main Menu 14 Ω 8Ω | Textbook Table of...
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- Spring '12