I vs i1 r1 i2 r2 v v clearly the two resistors

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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 | e-Text 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 WYE-DELTA 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 | e-Text 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.

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