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Unit Five: Series Circuits

ET115 DC Electronics. Unit Five: Series Circuits. John Elberfeld JElberfeld@itt-tech.edu WWW.J-Elberfeld.com. Schedule. Unit Topic Chpt Labs Quantities, Units, Safety 1 2 (13) Voltage, Current, Resistance 2 3 + 16 Ohm’s Law 3 5 (35) Energy and Power 3 6 (41)

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Unit Five: Series Circuits

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  1. ET115 DC Electronics Unit Five:Series Circuits John Elberfeld JElberfeld@itt-tech.edu WWW.J-Elberfeld.com

  2. Schedule Unit Topic Chpt Labs • Quantities, Units, Safety 1 2 (13) • Voltage, Current, Resistance 2 3 + 16 • Ohm’s Law 3 5 (35) • Energy and Power 3 6 (41) • Series Circuits Exam I 4 7 (49) • Parallel Circuits 5 9 (65) • Series-Parallel Circuits 6 10 (75) • Thevenin’s, Power Exam 2 6 19 (133) • Superposition Theorem 6 11 (81) • Magnetism & Magnetic Devices 7 Lab Final • Course Review and Final Exam

  3. Unit 5 Objectives - I • Identify a series resistive circuit. • Determine total resistance, current, and power in a series resistive circuit. • State Kirchhoff’s voltage law. • Solve for an unknown voltage in a circuit using Kirchhoff’s voltage law (KVL). • State the voltage divider formula. • Apply the voltage-divider formula to series circuits to find an unknown quantity (either a voltage or resistance).

  4. Unit 5 Objectives – II • Calculate the range of output voltages when a potentiometer is used as a voltage-divider. • Construct basic DC circuits on a protoboard. • Use a digital multimeter (DMM) to measure a predetermined low voltage on a power supply.

  5. Unit 5 Objectives – III • Measure resistances and voltages in a DC circuit using a DMM. • Apply Ohm’s Law, Thevenin’s theorem, KVL and KCL to practical circuits. • Troubleshoot circuits constructed in Multisim exercises using simulated instruments.

  6. Reading Assignment • Read and study • Chapter 4: Series Circuits:Pages 109-147

  7. Lab Assignment • Lab Experiment 7:“Series Circuits,” page 49 • Complete all measurements, graphs, and questions and turn in your lab before leaving the room

  8. Written Assignments • Complete the Unit 5 Homework sheet • Show all your work! • Be prepared for a quiz on questions similar to those on the homework.

  9. Series Circuit • A series circuit has one path for current flow. • The current is the same at any point in the circuit.

  10. SERIES CIRCUITS • Total resistance in a series circuit is the summation of the individual resistor values: RT = R1 + R2 + R3 …. + Rn Where n = the number of resistors

  11. OHM’S LAW • Ohm’s Law applies to the total circuit • Total resistance in a series circuit is equal to the total circuit voltage divided by the total current • ITis the same at every point in the circuit VT = ITRT IT = VT /RT

  12. Single Resistor Circuit • Single resistor example (Simplest) • V = I R or R = V/I • R = 10V/2A = 5  ?

  13. V = 15V I = ? R = 1kΩ Find the Current Voltage = 15 V Resistance = 1 k I = _______

  14. V = 15V I = ? R = 1kΩ Find the Current Voltage = 15 V Resistance = 1 k I = _______

  15. Find the Voltage Resistance = 10 k Current = 4 mA Voltage = ______ V = ? V I = 4mA R = 10kΩ

  16. Find the Voltage Resistance = 10 k Current = 4 mA Voltage = ______ V = ? V I = 4mA R = 10kΩ

  17. V = 60V I = 4mA R = ?Ω Find the Resistance Current = 4 mA Voltage = 60 V Resistance = _______

  18. V = 60V I = 4mA R = ?Ω Find the Resistance Current = 4 mA Voltage = 60 V Resistance = _______

  19. Multiple Resistor Example • Series circuit comprised of resistors: • To calculate the total resistance we use the formula RT = R1 + R2 + R3 + etc. • The total resistance for the figure is: • RT= 10Ω + 20Ω + 30Ω = 60 OHMS

  20. Br Bk Bk Br Gy Bk V = 120V R R Bk Three Resistors • Brown Black Black = ___________ • Brown Grey Black = ___________ • Red Red Black = ___________ • Total Resistance = ___________

  21. Simplify the Circuit • To make life easier, you can replace many resistors in series in the circuit with a single resistor that has the same effect on the circuit values as all the resistors it replaced • The value of the replacement resistor is equal to the sum of all the series resistors that it is replacing

  22. The BIG Idea • In a pure series circuit, the current in every resistor is the same – the same as the current that leaves the battery

  23. R1 R2 V = 95 V R3 Find the Current mA mA mA mA • If the current in the bottom left Ammeter is 5 mA, what is the current in the: • Bottom Right = ______________ • Upper Left = ______________ • Upper Right = ______________

  24. Find the Current R1 = 82 Ω R2= 56 Ω V = 120V Replacement Resistor V = 120V R = ???? Ω I = ?mA

  25. Find the Current R1 = 82 Ω R2= 56 Ω V = 120V Replacement Resistor V = 120V R = 138 Ω I = ?mA RT = 82 Ω + 56 Ω = 138 ΩIT = VT/RT = 120V / 138 Ω = 870 mA

  26. Find the Current R1 = Gn Be Br R1 = ______ R2 = ______ R2= Br Bk R V = 120V RT = R1 + R2 = __________________

  27. Find the Current R1 = Gn Be Br R1 = 560 Ω R2 = 1 kΩ R2= Br Bk R V = 120V Replacement Resistor V = 120V R = 1.56 kΩ I = ?mA RT = 560 Ω + 1 kΩ = 1.56 kΩIT = VT/RT = 120V / 1.56 kΩ = 76.8 mA

  28. Find the Current R1 = O O Bk R1 = ______ R2 = ______ R2= Y V Bk V = 120V RT = R1 + R2 = __________________

  29. Find the Current R1 = O O Bk R1 = 33 Ω R2 = 47 Ω R2= Y V Bk V = 120V Replacement Resistor V = 120V R = 80 Ω I = ?mA RT = 33 Ω + 47 Ω = 80 ΩIT = VT/RT = 120V / 80 Ω = 1.5 A

  30. R1 = Br Gn R R2= R R R V = 95V R3 = Br Bk O Find the Current R1 = ______ R2 = ______ R3 = ______ RT = R1 + R2 + R3 = __________________

  31. R1 = 1.5 kΩ R2= 2.2 kΩ V = 95 V R3 = 10 kΩ Find the Current Replacement Resistor V = 95 V R = 13.7 kΩ I = ?mA RT = 1.5 kΩ + 2.2 kΩ + 10 kΩ = 13.7 kΩIT = VT/RT = 95V / 13.7 kΩ = 6.93 mA

  32. Multiple Resistors • What is the total resistance of twelve 5.6 kΩ resistors in series? • RT = 12 x 5.6 kΩ = 67.2 kΩ • What is the total resistance of six 47 Ω resistors, eight 100 Ω resistors and two 22 Ω resistors in series? • _________________

  33. Multiple Resistors • What is the total resistance of twelve 5.6 kΩ resistors in series? • RT = 12 x 5.6 kΩ = 67.2 kΩ • What is the total resistance of six 47 Ω resistors, eight 100 Ω resistors and two 22 Ω resistors in series? • 1.126 kΩ

  34. Missing Resistor • Five resistors in series have a total resistance of 20 kΩ. • The value of four of the resistors are 4.7 kΩ, 1.0 kΩ, 2.2 kΩ, and 3.9 kΩ. • What is the value of the fifth resistor? • R5 = ________________

  35. Missing Resistor • Five resistors in series have a total resistance of 20 kΩ. • The value of four of the resistors are 4.7 kΩ, 1.0 kΩ, 2.2 kΩ, and 3.9 kΩ. • What is the value of the fifth resistor? • 20 kΩ = 4.7kΩ+1.0kΩ+2.2kΩ+3.9kΩ+X • 20 kΩ = 11.8kΩ+X • X = 20 kΩ - 11.8kΩ = 8.2kΩ

  36. R1 = 10kΩ R2= 20kΩ V = 120V R3 = 30kΩ Voltage Drop • V=IR (Ohm’s Law) applies to each resistor in the circuit • I = 2 mA = the same current in each and every resistor in a series circuit RT = 60kΩ IT=VT/RT IT = 120 V/ 60kΩ IT = 2 ma + -

  37. Voltage Drop R1 = 10kΩV = 2 ma 10k Ω =20 V • I = 2 mA • VA = V1 + V2 + V3 = 20V + 40V + 60V = 120 V • The sum of the voltage drops across all the resistors adds up to the input voltage + - + - R2 = 20kΩV = 2ma 20k ΩV= 40 V + - V = 120V - + R3 = 30kΩV = 2ma 30k Ω = 60 V

  38. Voltage Drop in a Series Resistive Circuit • Voltage drop in the series circuit is given by the sum of the individual voltage drops across all the resistors:

  39. RT = 8.8kΩ IT=VT/RT IT = 5.5 V/8.8kΩ IT = 625 µa Voltage Drop R1 = 2.2 kΩV1 = ???? + - + - R2 = 5.6 kΩV2 = ????? + - V = 5.5 V - + R3 = 1.0 kΩV3 = ??????

  40. RT = 8.8kΩ IT=VT/RT IT = 5.5 V/8.8kΩ IT = 625 µa Voltage Drop R1 = 2.2 kΩV1 = 625 µa 2.2 kΩ =1.375 V + - + - R2 = 5.6 kΩV2 = 625 µa 5.6 kΩ =3.5 V + - V = 5.5 V - + R3 = 1.0 kΩV3 = 625 µa 1.0 kΩ = 625 mV What is the sum of the voltage drops in the resistors?

  41. RT = 8.8kΩ IT=VT/RT IT = 5.5 V/8.8kΩ IT = 625 µa Voltage Drop R1 = 2.2 kΩV1 = 625 µa 2.2 kΩ =1.375 V • VT = V1 + V2 + V3 = 1.375V + 3.5V + 625m V = 5.5 V • The sum of the voltage drops across all the resistors adds up to the input voltage + - + - R2 = 5.6 kΩV2 = 625 µa 5.6 kΩ =3.5 V + - V = 5.5 V - + R3 = 1.0 kΩV3 = 625 µa 1.0 kΩ = 625 mV

  42. Kirchhoff’s Voltage Law • The sum of all voltage drops in a closed loop is equal to the value of the applied voltage • This deals with magnitudes • The algebraic sum of all the voltage drops and all the voltage sources in any closed loop equals 0 • This includes the sign of the voltage

  43. Kirchhoff’s Voltage Law

  44. R1 = 1 MΩ R2 = 2.2 MΩ V = 16V R3 = 560 kΩ Sample Problems - 1 + -

  45. R1 = 1 MΩ R2 = 2.2 MΩ V = 16V R3 = 560 kΩ Sample Problems - 1 + -

  46. Power Calculations • Power = Voltage x Current = Watts • P = VI • The more electric power a motor uses, the more work it can do per second • Combining with Ohm’s Law: • P = I2R P = V2/R

  47. Power in a Series Circuit • P = I2R • Because current is the same at every point in a series circuit, the resistance with the smallest value will also dissipate the smallest power value. • The largest resistor in the circuit will dissipate the largest amount of power.

  48. Power in a Series Circuit • Since the current is the same at any point in a series circuit, the equation P = I 2 R is often the best equation to use when both I and R are known.

  49. Power in a Series Circuit • The total power dissipated in a series circuit is also the amount of power the Power Source must deliver. • The power supplied is equal to the total power dissipated in the circuit elements • This may also be expressed as: PT = PR 1 + PR 2 … + PR n

  50. R1 = 4.7 kΩ R2 = 4.7 kΩ V = 48 V R3 = = 4.7 kΩ Sample Problems - 2 + -

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