### Series Circuit

Chapter 4 Chapter 4 Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Series circuits Summary All circuits have three common attributes. These are: 1. A source of voltage. 2. A load. 3. A complete path. VS + R3 R1 R2 Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Series circuits Summary A series circuit is one that has only one current path. R1 R1 R2 R3 VS R3 R2 VS R1 R2 R3 VS Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Summary Series circuit rule for current:

Because there is only one path, the current everywhere is the same. For example, the reading on the first ammeter is 2. 0 mA, What do the other meters read? + 2. 0 mA _ VS _ R1 + 2. 0 mA _ R2 2. 0 mA + _ 2. 0 mA + © Copyright 2007 Prentice-Hall Electric Circuits Fundamentals – Floyd Chapter 4 Series circuits Summary The total resistance of resistors in series is the sum of the individual resistors. For example, the resistors in a series circuit are 680 ? , 1. 5 k? , and 2. 2 k?. What is the total resistance? R1 VS 12 V 680 ? R2 1. 5 k? 4. 38 k? R3 2. 2 k?

Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Series circuit Summary VS 12 V R1 680 ? R2 1. 5 k? R3 2. 2 k? Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a series circuit. Continuing with the previous example, complete the parameters listed in the Table. I1= 2. 74 mA I2= 2. 74 mA I3= 2. 74 mA IT= 2. 74 mA R1= 0. 68 k? R2= 1. 50 k? R3= 2. 20 k? RT= 4. 38 k? V1= 1. 86 V V2= 4. 11 V V3= 6. 03 V VS= 12 V P1= 5. 1 mW P2= 11. 3 mW P3= 16. 5 mW PT= 32. 9 mW © Copyright 2007 Prentice-Hall

Electric Circuits Fundamentals – Floyd Chapter 4 Summary Kirchhoff’s voltage law Kirchhoff’s voltage law (KVL) is generally stated as: The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path. KVL applies to all circuits, but you must apply it to only one closed path. In a series circuit, this is (of course) the entire circuit. Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Summary VS 12 V R1 680 ? R2 1. 5 k? Kirchhoff’s voltage law R3 2. 2 k?

Notice in the series example given earlier that the sum of the resistor voltages is equal to the source voltage. I1= 2. 74 mA I2= 2. 74 mA I3= 2. 74 mA IT= 2. 74 mA R1= 0. 68 k? R2= 1. 50 k? R3= 2. 20 k? RT= 4. 38 k? V1= 1. 86 V P1= 5. 1 mW V2= 4. 11 V P2= 11. 3 mW V3= 6. 03 V P3= 16. 5 mW VS= 12 V PT= 32. 9 mW © Copyright 2007 Prentice-Hall Electric Circuits Fundamentals – Floyd Chapter 4 Summary Voltage divider rule The voltage drop across any given resistor in a series circuit is equal to the ratio of that resistor to the total resistance, multiplied by source voltage.

VS Assume R1 is twice the size of R2. What is the voltage across R1? 8 V 12 V R1 R2 Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Voltage divider Summary R1 15 k? VS + 20 V R2 10 k? What is the voltage across R2? The total resistance is 25 k?. Applying the voltage divider formula: ? R2 V2 = ? ? RT ? ? 10 k? ? ? VS = ? ? 20 V = 8. 0 V ? 25 k? ? ? Notice that 40% of the source voltage is across R2, which represents 40% of the total resistance. Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4

Voltage divider Summary Voltage dividers can be set up for a variable output using a potentiometer. In the circuit shown, the output voltage is variable. VS + 15 V R1 20 k? R2 10 k? What is the largest output voltage available? 5. 0 V VOUT Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Summary R1 470 ? VS + 20 V R2 330 ? Power in Series Circuits Use the voltage divider rule to find V1 and V2. Then find the power in R1 and R2 and PT. Applying the voltage divider rule: ? 470 ? ? V1 = ? ? 20 V = 11. 75 V ? 800 ? ? ? 330 ? V2 = ? ? 20 V = 8. 25 V ? 800 ? ? The power dissipated by each resistor is: P= 1 (11. 75 V ) 2 470 ? 2 ( 8. 25 V ) = 0. 21 W P2 = 330 ? = 0. 29 W } PT = 0. 5 W Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Summary A VS + 12 V R1 5. 0 k? B R2 10 k? C Voltage measurements Voltage is relative and is measured with respect to another point in the circuit. Voltages that are given with respect to ground are shown with a single subscript. For example, VA means the voltage at point A with respect to ground (called reference ground).

VB means the voltage at point B with respect to ground. VAB means the voltage between points A and B. What are VA, VB, and VAB for the circuit shown? VA = 12 V VB = 8 V VAB = 4 V Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Summary A R1 5. 0 k? B R2 10 k? C Voltage measurements Ground reference is not always at the lowest point in a circuit. Assume the ground is moved to B as shown. VS + 12 V What are VA, VB, and VC for the circuit? VA = 4 V VB = 0 V VC = ? 8 V Has VAB changed from the previous circuit?

No, it is still 4 V Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Selected Key Terms Series In an electric circuit, a relationship of components in which the components are connected such that they provide a single path between two points. Kirchhoff’s A law stating that (1) the sum of the voltage voltage law drops around a closed loop equals the source voltage in that loop or (2) the algebraic sum of all of the voltages (drops and source) is zero. Voltage divider A circuit consisting of series resistors across which one or more output voltages are taken.

Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall Chapter 4 Reference ground Selected Key Terms The metal chassis that houses the assembly or a large conductive area on a printed circuit board is used as a common or reference point; also called common. A circuit condition in which the current path is broken. A circuit condition in which there is zero or an abnormally low resistance between two points; usually an inadvertent condition. Open Short Electric Circuits Fundamentals – Floyd © Copyright 2007 Prentice-Hall