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Series Circuits Assessment and Characteristics

Assess your understanding of series circuits, Ohm’s Law, voltage relationships, and Kirchhoff’s laws with these questions and activities. Explore voltage dividers and resistance calculations in a team setting for practical applications.

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Series Circuits Assessment and Characteristics

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  1. Retention Assessment • Put your books away and take out a sheet of paper. Answer the questions below to the best of your ability. • When you have finished, fold your paper in half and raise your hand to have your paper collected. • Your score will count toward In-Class activities EGR 101 1

  2. Quiz • 1. What is the relationship between current and charge? • 2. Express voltage in terms of charge, energy, and/or time. • 3. Express Power in terms of charge, energy, and/or time. • 4. State Ohm’s Law. EGR 101 2

  3. Today’s AgendaChapter 4 Series Circuits Voltage Divider 3

  4. Series Circuit • Series Circuit – a circuit that contains only one current path EGR 101 4

  5. Series Circuit Characteristics • Current Characteristics – the current through any element in a series circuit must equal the current through every other element in the circuit EGR 101 5

  6. A B C E D F Series Connections • Two elements are connected in series if ALL of the current of one element flows through the second. • Which of the following are in series? EGR 101 6

  7. Relation to Lab Activity • In the lab last week, for one of the circuits, you had 2 resistors connected as shown to the right (with different values) and a meter set on Ohms measuring them. Are the resistors in series? • What resistance would the multimeter read if you built this circuit? • What would the meter read if you put 10 22k-Ohm resistors in series? EGR 101 7

  8. Series Connection Characteristics • Total Series Resistance where RT = the total series resistance Rn = the highest-numbered resistor in series EGR 101 8

  9. Example Series Circuit V1 V2 • What is the total resistance? • What is the current, IT? • What is the voltage across each resistor? EGR 101 9

  10. Kirchhoff’s Voltage Law • Note, in the example on the previous page,Vs= V1 +V2 EGR 101 10

  11. Series Circuit Characteristics • Series circuits have the following voltage characteristic: where VS = the source (or total supply) voltage Vn = the voltage across the highest numbered resistor in the circuit EGR 101 11

  12. Voltage Relationships • Kirchhoff’s Voltage Law • The sum of the component voltages in a series circuit must equal the net source voltage • 1840 – German Physicist, Gustav Kirchhoff EGR 101 12

  13. Series Circuit Characteristics • Power Characteristics where PS = the source power PT = the total power dissipated by the circuit Pn = the power that is dissipated across the highest numbered resistor in the circuit EGR 101 13

  14. Team Activity # 1: Refer to Figure 4.45(d) on p. 125 of textbook Method 1: • Calculate the total resistance of the circuit, RT. • Calculate I using RT and Ohm’s Law. • Calculate the total power PT using Vs and I. Method 2: • Calculate I using Ohm’s Law. • Calculate the voltage across each resistance, V1, V2,V3 & V4. • Calculate the power in each resistor P1, P2, P3 & P4. EGR 101 14

  15. Comparison of Results • Questions: • Does the VTyou computed in Method 2 equal Vs from Method 1? • Does the sum of P1, P2, P3 & P4 equal PT from Method 1? EGR 101 15

  16. Voltage Notations • Single subscript, VA– indicates the voltage is measured from the specified point relative to ground • Two subscripts, VAB– indicates the voltage is measured from the first identified point to the second A } + VA _ A } + VAB _ } + B V? _ EGR 101 16

  17. Voltage Divider • The Voltage Divider Relationship– Often used to analyze a portion of a series circuit • Allows us to determine individual voltages RestofCircuit } A V1 } V2 } V3 B EGR 101 17

  18. Voltage Divider Relation • For a series combination of N resistors with Vs (VAB in previous slide) applied across them, the voltage across Rn is: where Rn = the resistor n of interest Vn = the voltage across across Rn RT = the total series resistance EGR 101 18

  19. Team Activity # 2: Refer to Figure 4.46(c) on p. 125 of textbook • Calculate the voltage across each resistor, R1, R2, & R3 by the Voltage Divider Method. • What is the resistance from point A to ground? • Calculate the current through each resistor using your results from step 1. • Calculate the current in the circuit based on Vs and total resistance. • Do your results from steps 3 and 4 agree? EGR 101 19

  20. The Potentiometer as a Voltage Divider • Audio Amplifier Application EGR 101 20

  21. Team Activity # 3: Refer to Figure 4.39(b) on p. 122 of textbook • Solve problem 12. EGR 101 21

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