Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 5

Chapter 5

Chapter 5

All circuits have three common attributes. These are:

Series circuits

1. A source of voltage.2. A load.3. A complete path.

A series circuit is one that has only one current path.

R1

VS R2

R3

+

Chapter 5

Series circuit rule for current:Because there is only one path, the current everywhere is the same. IT = IR1 = IR2 = IR3 =…= IRN

R2

R1

VS

+ _+ _

++ __

2.0 mA

For example, the reading on the first ammeter is 2.0 mA, What do the other meters read?

2.0 mA

2.0 mA2.0 mA

Chapter 5

Chapter 5

Chapter 5

Chapter 5

Series circuits

The total resistance of resistors in series isthe sum of the individual resistors.

RT = R1 + R2 + R3 +… + RN

4.38 k

For example, the resistors in a series circuit are 680 , 1.5 k, and 2.2 k. What is the total resistance?

R

R

2

3

R1

VS

680

2.2 k

1.5 k12 V

Chapter 5Series circuit

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= R1= 0.68 k V1= P1= I2= R2= 1.50 k V2= P2= I3= R3= 2.20 k V3= P3= IT= RT= 4.38 k VS= 12 V PT= 2.74 mA

2.74 mA2.74 mA2.74 mA 1.86 V

4.11 V6.03 V

5.1 mW11.3 mW16.5 mW32.9 mW

R

R

2

3

R1

VS

680

2.2 k

1.5 k12 VFor a constant source voltage, smaller valued resistors drop less voltage and dissipate less power than higher valued resistors.

Chapter 5

Voltage sources in series

Voltage sources in series add algebraically. For example, the total voltage of the sources shown is

+

+

+

9 V

9 V

9 V

27 V

9 VWhat is the total voltage if one battery is reversed?

Chapter 5

Kirchhoff’s voltage law 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. VS = V1 + V2 + V3 + …+ VN

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.KVL is also stated as the algebraic sum of all voltages (voltage drops and sources) around a single closed path in a circuit is equal to zero. 0 = -VS + V1 + V2 + V3 + …+ VN

Chapter 5Kirchhoff’s Voltage Law (KVL)

The total voltage is equalto the sum of the drops.

VT = V1 + V2 + V3 + V4 + V5

V1 V2V3

V4V5

VT

This is known as Kirchhoff’s voltage law (KVL).

The total voltage is equalto the sum of the drops.

VT = V1 + V2 + V3 + V4 + V5

V1 V2V3

V4V5

VT

V1 V2V3

V4V5

VT

This is known as Kirchhoff’s voltage law (KVL).

Chapter 5

The IR drops must add to equal the applied voltage (KVL).

VT = V1 + V2 + V3 + V4 + V5VT = IR1 + IR2 + IR3 + IR4 + IR5VT = 0.1 × 10 + 0.1 × 15 + 0.1 × 20 + 0.1 × 30 + 0.1 × 25VT = 1 V + 1.5 V + 2 V + 3 V + 2.5 V = 10 V

V1 V2V3

V4V5

VT = 10

10

20

15

25 30 0.1 A

Kirchhoff’s Voltage Law (KVL)

Chapter 5Polarity of IR Voltage Drops

Polarity of IR voltage drops. (a) Electrons flow into the negative side of V1 across R1. (b) Same polarity of V1 with positive charges into the positive side.

The polarity of the IR drop is the same, regardless of whether we consider electron flow or conventional current.

Chapter 5

Kirchhoff’s voltage law

Notice in the series example given earlier that the sum of the resistor voltages is equal to the source voltage.

I1= R1= 0.68 k V1= P1= I2= R2= 1.50 k V2= P2= I3= R3= 2.20 k V3= P3= IT= RT= 4.38 k VS= 12 V PT= 2.74 mA

2.74 mA2.74 mA2.74 mA 1.86 V

4.11 V6.03 V

5.1 mW11.3 mW16.5 mW32.9 mW

R

R

2

3

R1

VS

680

2.2 k

1.5 k12 V

Chapter 5

Assume R1 is twice the size of R2. What is the voltage across R1?

R1

R2R2

1VSVS

12 V

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 the source voltage.

8 V

ST

XRX V

RRV

VRRV

TR 12

321

1

Let R1 = 2ΩLet R2 = 1Ω

Chapter 5

What is the voltage across R2?

The total resistance is 25 kApplying the voltage divider formula:

22 S

T

10 k20 V 8 V25 k

RV VR

R1

VS R2+10 k

15 k

20 V

Voltage divider

Notice that 40% of the source voltage is across R2, which represents 40% of the total resistance.

Chapter 5

Voltage divider

Voltage dividers can be set up for a variable output using a potentiometer. In the circuit shown, the output voltage is variable.

What is the largest output voltage available?

VS

VOUT

R2

R1

+

10 k

20 k

15 V

5.0 V

Turn pot in maximum direction for maximum R. Then, V

kRkRV

TR 15

30102

2

Chapter 5 Total Power in a Series Circuit

– The power needed to produce current in each series resistor is used up in the form of heat.

– The total power used in the circuit is equal to the sum of the individual powers dissipated in each part of the circuit.

– Total power can also be calculated as VT × I

The sum of the individual powers P1 and P2 used in each resistance equals the total power PTproduced by the source.

Chapter 5

PT = P1 + P2 + P3 + P4 + P5

PT = I2R1 + I2R2 + I2R3 + I2R4 + I2R5

PT = 0.1 W + 0.15 W + 0.2 W + 0.3 W + 0.25 W = 1 W

Check: PT = VT × I = 10 V × 0.1 A = 1 W

P1 P2

P3

P4P5

VT = 10

10

20

15

25 30 0.1 A

Total Power in a Series Circuit

Chapter 5

Power in Series Circuits

Applying the voltage divider rule:

1470 20 V 11.75 V800

V

The power dissipated by each resistor is:

2

1

11.75 V0.29 W

470 P

Use the voltage divider rule to find V1 and V2. Then find the power in R1 and R2 and PT.

R1

VS R2+ 330

470

20 V

2330 20 V 8.25 V800

V 2

2

8.25 V0.21 W

330 P

PT = 0.5 W

Chapter 5

R1

VS R2+10 k

15 k

20 V

Voltage Divider derivation using Ohm’s Law

ST

R

T

SR

TR

VRRV

RRVV

RIV

22

22

22

To find VR2 using Ohm’s Law:

Replace IT with:

Rearrange

Chapter 5

Circuit Ground

The term “ground” typically means a common or reference point in the circuit.

Voltages that are given with respect to ground are shown with a single subscript. For example, VAmeans the voltage at point A with respect to 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?

VS

R2

R1

+

10 k

5.0 k

12 V

A

B

C

VA = 12 V VB = 8 V VAB = 4 V

Chapter 5 Troubleshooting: Opens in Series Circuits

• The Effect of an Open in a Series Circuit

Effect of an open in a series circuit. Open path between points P1 and P2 results in zero current in all parts of the circuit.

Chapter 5 Troubleshooting: Shorts in Series Circuits

• The Effect of a Short in a Series Circuit

When R2 is shorted in a series circuit, the total current increases from 1A to 1.333A. This causes an increase in the IR drop of the other resistors as well as their power dissipation.

Normally 25V

Normally 5V Normally 10V

Chapter 5

Circuit ground

Kirchhoff’s voltage law

Open

A law stating that (1) the sum of the voltage 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.

A circuit condition in which the current path is broken.

A method of grounding whereby 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 chassis ground.

Key Terms

Chapter 5

Series

Short

Voltage divider

A circuit condition in which there is zero or an abnormally low resistance between two points; usually an inadvertent condition.

A circuit consisting of series resistors across which one or more output voltages are taken.

Key Terms

In an electric circuit, a relationship of components in which the components are connected such that they provide a single path between two points.

Chapter 5Quiz

1. In a series circuit with more than one resistor, the current is

a. larger in larger resistors

b. smaller in larger resistors

c. always the same in all resistors

d. there is not enough information to say

Chapter 5Quiz

1. In a series circuit with more than one resistor, the current is

a. larger in larger resistors

b. smaller in larger resistors

c. always the same in all resistors

d. there is not enough information to say

Chapter 5Quiz

2. In a series circuit with more than one resistor, the voltage is

a. larger across larger resistors

b. smaller across larger resistors

c. always the same across all resistors

d. there is not enough information to say

Chapter 5Quiz

2. In a series circuit with more than one resistor, the voltage is

a. larger across larger resistors

b. smaller across larger resistors

c. always the same across all resistors

d. there is not enough information to say

Chapter 5Quiz

3. If three equal resistors are in series, the total resistance is

a. one third the value of one resistor

b. the same as one resistor

c. three times the value of one resistor

d. there is not enough information to say

Chapter 5Quiz

3. If three equal resistors are in series, the total resistance is

a. one third the value of one resistor

b. the same as one resistor

c. three times the value of one resistor

d. there is not enough information to say

Chapter 5Quiz

4. A series circuit cannot have

a. more than two resistors

b. more than one voltage source

c. more than one path

d. all of the above

Chapter 5Quiz

4. A series circuit cannot have

a. more than two resistors

b. more than one voltage source

c. more than one path

d. all of the above

Chapter 5Quiz

5. In a closed loop, the algebraic sum of all voltages (both sources and drops)

a. is 0

b. is equal to the smallest voltage in the loop

c. is equal to the largest voltage in the loop

d. depends on the source voltage

Chapter 5Quiz

5. In a closed loop, the algebraic sum of all voltages (both sources and drops)

a. is 0

b. is equal to the smallest voltage in the loop

c. is equal to the largest voltage in the loop

d. depends on the source voltage

Chapter 5Quiz

6. The current in the 10 k resistor is

a. 0.5 mA

b. 2 mA

c. 2.4 mA

d. 10 mA

VS

R2

R1

+

2.0 k

10 k

24 V

Chapter 5Quiz

6. The current in the 10 k resistor is

a. 0.5 mA

b. 2 mA

c. 2.4 mA

d. 10 mA

VS

R2

R1

+

2.0 k

10 k

24 V

kV

RVII

T

STR

1224

1

Chapter 5Quiz

7. The output voltage from the voltage divider is

a. 2 V

b. 4 V

c. 12 V

d. 20 V

VS

VOUTR2

R1

+

2.0 k

10 k

24 V

Chapter 5Quiz

7. The output voltage from the voltage divider is

a. 2 V

b. 4 V

c. 12 V

d. 20 V

VS

VOUTR2

R1

+

2.0 k

10 k

24 V

VkRkRV

TR 24

120.22

2

Chapter 5Quiz

8. The smallest output voltage available from the voltage divider is

a. 0 V

b. 1.5 V

c. 5.0 V

d. 7.5 V

VS

VOUT

R2

R1

+

10 k

0 k

15 V

Chapter 5Quiz

8. The smallest output voltage available from the voltage divider is

a. 0 V

b. 1.5 V

c. 5.0 V

d. 7.5 V

VS

VOUT

R2

R1

+

10 k

0 k

15 V

Chapter 5Quiz

9. The total power dissipated in a series circuit is equal to the

a. power in the largest resistor

b. power in the smallest resistor

c. average of the power in all resistors

d. sum of the power in all resistors

Chapter 5Quiz

9. The total power dissipated in a series circuit is equal to the

a. power in the largest resistor

b. power in the smallest resistor

c. average of the power in all resistors

d. sum of the power in all resistors

Chapter 5Quiz

10. The meaning of the voltage VAB is the voltage at

a. Point A with respect to ground

b. Point B with respect to ground

c. The average voltage between points A and B.

d. The voltage difference between points A and B.

Chapter 5Quiz

10. The meaning of the voltage VAB is the voltage at

a. Point A with respect to ground

b. Point B with respect to ground

c. The average voltage between points A and B.

d. The voltage difference between points A and B.