1. Communication Signals Series Circuits With Resistors Fox Valley Technical College Appleton, WI, USA 110/9/2015

2. Review: Series Circuit Characteristics Elements of a series circuit are connected in a string. A series circuit provides only one path for current flow from the + to the − terminals of the power source. The same current passes through each device. Every node of a series circuit has one current inlet and one current outlet. 210/9/2015

3. Resistors Connected in Series It is easy to see that these resistor strings are each a series connection of resistors. R1R1 R2R2 R3R3 R4R4 R5R5 R6R6 R7R7 R8R8 R9R9 R 10 R 11 R 12 R 13 R 14 310/9/2015

4. Examples of Series Resistor Connections A B - + A B - + - A B + A B -+ A B - + In these circuits, it is not always easy to tell they are series connected resistors, How do we know? We observe carefully that there is only one current path in each circuit from A to B. 410/9/2015

5. Total Series Resistance Fox Valley Technical College Appleton, WI, USA 510/9/2015

6. Total resistance increases with each additional series resistor. (Notice the use of the battery & ground symbols here.) -+-+ 10Ω -+-+ 20Ω -+-+ 10Ω 30Ω 610/9/2015

7. Example of five resistors in series (V S stands for “source” voltage.) R5R5 R4R4 R3R3 R2R2 R1R1 VSVS 47Ω 10Ω 27Ω 100Ω 56Ω -+-+ 710/9/2015

8. Total Series Resistance If the resistor values are not all the same, then the total equivalent resistance R T is: R T = R 1 + R 2 +... +R n If the resistor values are all the same value R, then the total equivalent resistance R T is: R T = R + R + R... + R R T = n x R Where the T subscript stands for Total equivalent resistance. 810/9/2015

9. Example: Different resistors in series R5R5 R4R4 R3R3 R2R2 R1R1 VSVS 47Ω 10Ω 27Ω 100Ω 56Ω -+-+ 910/9/2015

10. Example: Identical resistors in series R5R5 R4R4 R3R3 R2R2 R1R1 VSVS 50Ω -+-+ 1010/9/2015

11. Measuring Series Resistors In–circuit 146kΩ VSVS R1R1 R2R2 R3R3 R4R4 10kΩ 33kΩ 47kΩ +-+- De-energize the circuit when measuring ohms! 1110/9/2015 Finding R 4 ??

12. Ohm’s Law & Voltages in Series Resistor Circuits Fox Valley Technical College Appleton, WI, USA 1210/9/2015

13. Ohm’s Law & Voltages in a Series Circuit  For any one resistor:  For total resistance:  But in a series circuit, the current is the same in all components, so: 1310/9/2015

14. One Resistor in a Series Circuit I R1 +V R1 − + V R2 − ITIT I R2 Resistors in a circuit are a key to knowing the current in that circuit. If we know the voltage across a single resistor, we can calculate the current in the resistor. If we know the current through one series resistor, we know the current in all the components in the series string. 1410/9/2015

15. PRACTICE: Find the current I T in all the components. Find V R2, the voltage on R 2. I R1 +4V− + V R2 − ITIT I R2 VSVS 9V R 1 = 1KΩ R 2 = 470Ω Ohm’s Law Series Circuits Ohm/s Law 1510/9/2015

16. Generalized Series Resistor Circuit But with resistors, we now have Ohm’s Law to work with also: +V 1 −+V 2 −+V 3 −+V 4 −+V n − VSVS ITIT I1I1 I2I2 I3I3 I4I4 InIn R1R1 R2R2 R3R3 R4R4 RnRn Therefore: 1610/9/2015

17. PRACTICE: Find I T R4R4 R3R3 R2R2 R1R1 VSVS 10Ω 15Ω 18Ω82Ω 25v ITIT 1710/9/2015

18. How would you find the values of these unlabeled resistors? Assume you have a power supply, an ammeter, and a voltmeter to help you. 1810/9/2015

19. Is this what you had in mind? Measuring each resistor voltage and dividing by the total circuit current we can determine each resistor value. Power Supply 12 V 2.5v 25mA R1R1 R2R2 R3R3 R4R4 3v 4.5v 2v 1910/9/2015

20. Resistors and Kirchhoff’s Voltage Law Fox Valley Technical College Appleton, WI, USA 2010/9/2015

21. Sum of n voltage drops equals the source voltage. V S = V1V1 V2V2 V3V3 VNVN -+-+ -+-+ -+-+ -+-+ -+-+ 2110/9/2015

22. Series Resistor Voltage Dividers Fox Valley Technical College Appleton, WI, USA 2210/9/2015

23. Two Resistor Voltage Divider Can we find V 1 and V 2 without first finding I T ? +-+- +-+- VSVS V1V1 V2V2 R2R2 R1R1 ITIT +-+- The source voltage is applied between these two terminals. This notation is equivalent to a battery symbol. In words: The voltage across one of two series resistors is the ratio of the value of the resistor to the total circuit resistance times the total source voltage. 2310/9/2015

24. Example: Two Resistor Voltage Divider 10v 100Ω 50Ω +-+- R T =150Ω R1R1 R2R2 2410/9/2015

25. A Multiple Resistor Voltage Divider (The same formula still applies.) VSVS V1V1 V2V2 V3V3 V4V4 V5V5 R1R1 R2R2 R3R3 R4R4 R5R5 I +-+- +-+- +-+- +-+- +-+- +-+- 2510/9/2015

26. The Potentiometer as a Voltage Divider Fox Valley Technical College Appleton, WI, USA 2610/9/2015

27. The Potentiometer as a Voltage Divider Potentiometer 3 2 1 1 2 3 VSVS +-+- 1 2 3 VSVS +-+- 2710/9/2015

28. Adjusting the Voltage Divider 5.0v VSVS +-+- 1 2 3 10v 9.5v VSVS +-+- 1 2 3 10v 2.0v VSVS +-+- 1 2 3 10v 2810/9/2015

29. A voltage divider used for volume control Audio Amplifier IF Amplifier Detector Volume Control 2910/9/2015

30. The Voltage Divider as a Voltage Reference Voltage Divider R1R1 R2R2 VSVS There is a lower voltage at this point which can be used as a voltage reference for another circuit. It cannot be used as a power source however. 3010/9/2015