EECS
2015+1-1,2,3+all.pdf

# Determine which resistors are in series the same

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Determine which resistors are in series (the same current flows through them all, without any bypass); these are resistors R3 and (R1||R2) a. Calculate their equivalent resistance (sum of individual resistances): it equals 15 Ω b. Replace these resistors with their equivalent resistance Figure 6 shows the redrawn diagrams of the circuit and calculations of ࠵? !" Figure 6. Step-by-step calculations of the equivalent resistance between nodes A and C. 5) After we replaced R3 +(R1||R2) with a single 15- Ω resistor this equivalent resistance is in parallel with R4; thus the equivalent resistance of the entire circuit equals: ࠵? !" = !" ! × !" ! !" ! ! !" ! = !"# !" ࠵? = 6 ࠵? Note that the equivalent resistance values for the same circuit differ by 50%: they are 4 Ω and 6 Ω , depending on how the ohmmeter is connected to the circuit. Different connections of the ohmmeter create: i. Different routes for the current ii. Different combinations of parallel/series resistances iii. Different voltage divisions and current divisions iv. Different distributions of the electric power absorbed throughout the circuit. Book Page 78

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EE for the 21 st century Review the basics 1-1-7 Combined series and parallel © 2015 Alexander Ganago Page 9 of 12 Last printed 2015-07-24 6:23 PM File: 2015 1-1-7 Comb SP.docx File: 2015 1-1-7 Comb SP.docx T YPICAL PROBLEMS FOR SELF - ASSESSMENT Problem 1 This diagram includes 3 resistors and labels for the currents and voltages. In the following statements, P 10 denotes the power absorbed by the 10- Ω resistor, etc. Consider the following statements about this circuit and choose the correct one. If an algebraic solution seems too hard, use a numerical value such as V Total = 10 V. A. V 10 > V 20 B. I 30 > I 20 C. P 10 > P 20 D. More than one statement A-C are correct E. None of the statements A-C is correct. Problem 2 In the circuit of Figure 1, the equivalent resistance equals R eq = 300 Ω , and the resistances are: R 2 = 400 Ω R 3 = 600 Ω . The unknown resistance R 1 equals: A. 428.6 Ω B. 771.4 Ω C. 200 Ω D. 60 Ω E. 600 Ω Book Page 79
EE for the 21 st century Review the basics 1-1-7 Combined series and parallel © 2015 Alexander Ganago Page 10 of 12 Last printed 2015-07-24 6:23 PM File: 2015 1-1-7 Comb SP.docx Problem 3 In the circuit of Figure 1, the equivalent resistance equals R eq = 200 Ω , the known resistances are: R 1 = 150 Ω R 2 = 240 Ω . The unknown resistance R 3 equals: A. 41.38 Ω B. 63.16 Ω C. 25.86 Ω D. None of the above answers is within 10% of the correct answer. E. With the given R 1 and R 2 the given equivalent resistance cannot be obtained, regardless of the value of R 3 Book Page 80

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EE for the 21 st century Review the basics 1-1-7 Combined series and parallel © 2015 Alexander Ganago Page 11 of 12 Last printed 2015-07-24 6:23 PM File: 2015 1-1-7 Comb SP.docx C ON Q UEST = C ONCEPTUAL QUESTIONS [Inspired by Eric Mazur] Students built a circuit with two identical batteries and two identical lamps. They worked with this circuit, then added a third lamp, identical to the others, as shown in the Figure below.
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• Fall '07
• Ganago
• Electric charge, Alexander Ganago

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