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Unformatted text preview: k Table of Contents  Problem Solving Workbook Contents VS = i1 R 1 = i 2 R 2
V
V
i1 = S
i2 = S
and
R1
R2
Using KCL, i = i1 + i 2
Now use the equations for i1 and i 2 to find i in terms of the source voltage and resistors. i= 1
R + R2 VS VS
1 = VS 1 +
= VS +
R1 R 2 R1 R 2 R1 R 2 R1 R 2 i
VS = R1 + R 2 Then, To find the branch currents, substitute the equation for VS into the equations for i1 and i 2 . i1 = 1 R1 R 2 i
R1 R1 + R 2 i2 = R2 i
i1 = R1 + R 2 1 R1 R 2 i
R 2 R1 + R 2 R1 i
i2 = R1 + R 2 Thus, it is clear that the current entering the node where two resistors are connected in parallel
divides proportionately between the two resistors. The proportionality is equal to the value of the
opposite resistor divided by the sum of the resistances times the incoming current. It should be
noted that this current division property only works for two resistors in parallel. If you have more
than two, you need to use a different process to find how the currents divide. Problem 2.14 Determine R eq for Figure 2.1. 15 Ω 10 Ω 8Ω 4Ω Req
30 Ω 10 Ω 4Ω 12 Ω 12 Ω 8Ω Figure 2.1 Req  v v 25 Ω  eText Main Menu  Textbook Table of Contents  R eq = 25 ohms Problem Solving Workbook Contents Using current division, determine i1 and i 2 in Figure 2.1. Problem 2.15 40 Ω R
i1 7A
i2
VS +
− 30 Ω Figure 2.1 i1 = 3 amps i 2 = 4 amps WYEDELTA TRANSFORMATIONS
The following is a summary of the conversions between wye and delta connected loads.
Given the following resistor network, the Y∆ equations are listed in the left column and the ∆Y
equations are listed in the right column. Rc a b
R2 R1 Ra Rb R3 R 1R 2 + R 2 R 3 + R 3 R 1
R1
R R + R 2 R 3 + R 3R1
Rb = 1 2
R2
R R + R 2 R 3 + R 3R1
Rc = 1 2
R3
Ra = R bRc
Ra + Rb + Rc
RaRc
R2 =
Ra + Rb + Rc
RaRb
R3 =
Ra + Rb + Rc
R1 =  v v c  eText Main Menu  Textbook Table of Contents  Problem Solving Workbook Contents Find R eq for Figure 2.1. Problem 2.16 10 Ω
2Ω 14 Ω
4Ω Req 5Ω 8Ω Figure 2.1
Carefully DEFINE the problem.
Each resistor has a value and the equivalent resistance is shown to be the resistance of the
network at the dotted...
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This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.
 Spring '12
 bkav

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