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 Ω, 1.5 kΩ, and 2.2 kΩ. What is the total resistance? R1 VS 12 V

680 Ω

R2 1.5 kΩ

4.38 kΩ

R3

2.2 kΩ

Electric Circuits Fundamentals - Floyd

© Copyright 2007 Prentice-Hall

Chapter 4

Series circuit

Summary

VS 12 V

R1

680 Ω

R2 1.5 kΩ

R3

2.2 kΩ

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 kΩ R2= 1.50 kΩ R3= 2.20 kΩ RT= 4.38 kΩ 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 Ω

R2 1.5 kΩ

Kirchhoff’s voltage law

R3

2.2 kΩ

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 kΩ R2= 1.50 kΩ R3= 2.20 kΩ RT= 4.38 kΩ 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 kΩ VS + 20 V R2 10 kΩ

What is the voltage across R2?

The total resistance is 25 kΩ. Applying the voltage divider formula:

⎛ R2 V2 = ⎜ ⎝ RT

⎞ ⎛ 10 kΩ ⎞ ⎟ VS = ⎜ ⎟ 20 V = 8.0 V ⎝ 25 kΩ ⎠ ⎠

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 kΩ R2 10 kΩ

What is the largest output voltage available? 5.0 V

VOUT

Electric Circuits Fundamentals - Floyd

© Copyright 2007 Prentice-Hall

Chapter 4

Summary

R1 470 Ω VS + 20 V R2 330 Ω

Power in Series...