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Chapter 7 Chapter 7 Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary Combination circuits Most practical circuits have combinations of series and parallel components. You can frequently simplify analysis by combining series and parallel components. An important analysis method is to form an equivalent circuit. An equivalent circuit is one that has characteristics that are electrically the same as another circuit but is generally simpler. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary Combination circuits For example: R1 1.0 k R2 is equivalent to R1 2.0 k 1.0 k There are no electrical measurements that can distinguish the boxes. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary Combination circuits Another example: is equivalent to R1 R2 1.0 k 1.0 k R1,2 500 There are no electrical measurements that can distinguish the boxes. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary is equivalent to R1 1.0 k R3 R 1,2 R3 R2 4.7 k 3.7 k 4.7 k 2.7 k is equivalent to R1,2,3 2.07 k Principles of Electric Circuits - Floyd There are no electrical measurements that can distinguish between the three boxes. © Copyright 2006 Prentice-Hall Chapter 7 Summary Combination circuits Kirchhoff’s voltage law and Kirchhoff’s current law can be applied to any circuit, including combination circuits. So will For example, this path! R2 applying KVL, the 2 470 path shown will have a sum of 0 V. VS 5.0 V R11 270 R4 100 R3 330 R6 Start/Finish Principles of Electric Circuits - Floyd Start/Finish R5 100 100 © Copyright 2006 Prentice-Hall Chapter 7 Summary Kirchoff’s current law can also be applied to the same circuit. What are the readings for node A? I + I - 26.5 mA + A I VS 5.0 V + + 8.0 mA R2 470 R4 - 18.5 mA 100 R1 270 R3 330 R6 R5 100 100 Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary Combination circuit VS + 10 V R1 270 R2 330 R3 470 Tabulating current, resistance, voltage and power is a useful way to summarize parameters. Solve for the unknown quantities in the circuit shown. I1= 21.6 mA I2= 12.7 mA I3= 8.9 mA IT= 21.6 mA R1= 270 R2= 330 R3= 470 RT= 464 Principles of Electric Circuits - Floyd V1= 5.82 V P1= 126 mW V2= 4.18 V P2= 53.1 mW V3= 4.18 V P3= 37.2 mW VS= 10 V PT= 216 mW © Copyright 2006 Prentice-Hall Chapter 7 Summary Kirchhoff’s laws can be applied as a check on the answer. R1 270 VS + 10 V R2 330 R3 470 Notice that the current in R1 is equal to the sum of the branch currents in R2 and R3. The sum of the voltages around the outside loop is zero. I1= 21.6 mA I2= 12.7 mA I3= 8.9 mA IT= 21.6 mA R1= 270 R2= 330 R3= 470 RT= 464 Principles of Electric Circuits - Floyd V1= 5.82 V P1= 126 mW V2= 4.18 V P2= 53.1 mW V3= 4.18 V P3= 37.2 mW VS= 10 V PT= 216 mW © Copyright 2006 Prentice-Hall Chapter 7 Loading effect of a voltmeter Summary VS + 10 V R1 470 k + 4.04 10 VV R2 Assume VS = 10 V, but the + 4.04 V 47 0 k meter reads only 4.04 V when it is across either R1 or R2. Can you explain what is happening? All measurements affect the quantity being measured. A voltmeter has internal resistance, which can change the resistance of the circuit under test. In this case, a 1 M internal resistance of the meter accounts for the readings. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary Wheatstone bridge The Wheatstone bridge consists R3 R1 VS of four resistive arms forming Output two voltage dividers and a dc voltage source. The output is R2 R4 taken between the dividers. Frequently, one of the bridge resistors is adjustable. When the bridge is balanced, the output voltage is zero, and the products of resistances in the opposite diagonal arms are equal. + - Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Summary Wheatstone bridge R3 330 Output - Principles of Electric Circuits - Floyd VS 12 V + Example: What is the value of R2 if the bridge is balanced? 384 R1 470 R2 R4 270 © Copyright 2006 Prentice-Hall Chapter 7 Key Terms Balanced bridge A bridge circuit that is in the balanced state is indicated by 0 V across the output. Bleeder current The current left after the load current is subtracted from the total current into the circuit. Load An element (resistor or other component) connected across the output terminals of a circuit that draws current from the circuit. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Key Terms Unbalanced A bridge circuit that is in the unbalanced state bridge is indicated by a voltage across the output that is proportional to the amount of deviation from the balanced state. Wheatstone A 4-legged type of bridge circuit with which bridge an unknown resistance can be accurately measured using the balanced state. Deviations in resistance can be measured using the unbalanced state. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Quiz 1. Two circuits that are equivalent have the same a. number of components b. response to an electrical stimulus c. internal power dissipation d. all of the above Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Quiz 2. If a series equivalent circuit is drawn for a complex circuit, the equivalent circuit can be analyzed with a. the voltage divider theorem b. Kirchhoff’s voltage law c. both of the above d. none of the above Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Quiz 3. For the circuit shown, a. R1 is in series with R2 - c. R2 is in series with R3 VS + b. R1 is in parallel with R2 R1 R2 R3 d. R2 is in parallel with R3 Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Quiz 4. For the circuit shown, R4 a. R1 is in series with R2 R1 b. R4 is in parallel with R1 Principles of Electric Circuits - Floyd - d. none of the above + c. R2 is in parallel with R3 VS R2 R3 © Copyright 2006 Prentice-Hall Chapter 7 Quiz 5. The total resistance, RT, of the group of resistors is a. 1.0 k R1 b. 2.0 k c. 3.0 k d. 4.0 k 500 1.0 k R3 2.0 k RT R5 500 Principles of Electric Circuits - Floyd R2 R4 1.0 k © Copyright 2006 Prentice-Hall Chapter 7 Quiz 6. For the circuit shown, Kirchhoff's voltage law a. applies only to the outside loop b. applies only to the A junction. c. can be applied to any closed path. d. does not apply. VS + 10 V R1 270 A R2 330 Principles of Electric Circuits - Floyd R3 470 © Copyright 2006 Prentice-Hall Chapter 7 Quiz 7. The effect of changing a measured quantity due to connecting an instrument to a circuit is called a. loading b. clipping c. distortion d. loss of precision Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall Chapter 7 Quiz 8. An unbalanced Wheatstone bridge has the voltages shown. The voltage across R4 is a. 4.0 V d. 7.0 V Principles of Electric Circuits - Floyd - c. 6.0 V VS 12 V + b. 5.0 V R1 7.0 V R2 R3 + RL 1.0 V R4 © Copyright 2006 Prentice-Hall Chapter 7 Quiz 9. Assume R2 is adjusted until the Wheatstone bridge is balanced. At this point, the voltage across R4 is measured and found to be 5.0 V. The voltage across R1 will be a. 4.0 V d. 7.0 V Principles of Electric Circuits - Floyd + RL - - c. 6.0 V VS 12 V + b. 5.0 V R3 R1 R2 R4 5.0 V © Copyright 2006 Prentice-Hall Chapter 7 Quiz 10. For the circuit shown, if R3 opens, the voltage at point A will R1 270 a. decrease b. stay the same. c. increase. Principles of Electric Circuits - Floyd VS + 10 V A R2 330 R3 470 © Copyright 2006 Prentice-Hall Chapter 7 Quiz Answers: Principles of Electric Circuits - Floyd 1. b 6. c 2. c 7. a 3. d 8. a 4. d 9. d 5. b 10. c © Copyright 2006 Prentice-Hall