Communication Communication SignalsSignals

Series Series Circuits With Circuits With

ResistorsResistors

Fox Valley Technical CollegeAppleton, WI, USA

104/19/23

Review: Series Circuit Review: Series Circuit CharacteristicsCharacteristics

• 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.

204/19/23

Resistors Connected in SeriesResistors Connected in Series

It is easy to see that these resistor strings are each a series connection of resistors.

R1 R2

R3 R4 R5

R6 R7 R8 R9

R10 R11 R12 R13 R14

304/19/23

Examples of Series Resistor Examples of Series Resistor ConnectionsConnections

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.

404/19/23

Total Series ResistanceTotal Series Resistance

Fox Valley Technical CollegeAppleton, WI, USA

504/19/23

Total resistance increases with Total resistance increases with each additional series resistor.each additional series resistor.

(Notice the use of the battery & ground symbols here.)

-

+

10Ω 10Ω -

+

10Ω

10Ω

20Ω -

+ 10Ω

10Ω

10Ω 30Ω

604/19/23

Example of five resistors in Example of five resistors in seriesseries

(VS stands for “source” voltage.)

R5 R4

R3

R2R1

VS

47Ω 10Ω

27Ω

100Ω56Ω-

+

704/19/23

Total Series ResistanceTotal Series Resistance

• If the resistor values are not all the same, then the total equivalent resistance RT is:

RT = R1 + R2 + . . . +Rn

• If the resistor values are all the same value R, then the total equivalent resistance RT is: RT = R + R + R . . . + R RT = n x R

Where the T subscript stands for Total equivalent resistance.804/19/23

Example: Example: DifferentDifferent resistors in resistors in seriesseries

R5 R4

R3

R2R1

VS

47Ω 10Ω

27Ω

100Ω56Ω

-

+

904/19/23

T 1 2 3 4 5

T

T

R =R +R +R +R +R

R =56+100+27+10+47

R =240Ω

Example: Example: IdenticalIdentical resistors in resistors in seriesseries

R5 R4

R3

R2R1

VS

50Ω 50Ω

50Ω

50Ω50Ω

-

+

1004/19/23

T 1 2 3 4 5

T

T

T

R =R +R +R +R +R

R =50+50+50+50+50

R =50×5

R =250

Measuring Series Resistors In–Measuring Series Resistors In–circuitcircuit

146kΩ

VS

R1

R2

R3

R4

10kΩ

33kΩ

47kΩ

+

-

De-energize the circuitwhen measuring ohms!

1104/19/23

Finding R4

??

4 1 2 3

4 146 10 33 47

4 146 90 56

TR R R R R

R K K K K

R K K K

Ohm’s Law & Voltages Ohm’s Law & Voltages

in Series Resistor in Series Resistor CircuitsCircuits

Fox Valley Technical CollegeAppleton, WI, USA

1204/19/23

Ohm’s Law & Voltages in a Series Ohm’s Law & Voltages in a Series CircuitCircuit

For any one resistor:

For total resistance:

But in a series circuit, the current

is the same in all components, so:

RR

VI

R

TT

T

VI =

R

T RI I

1304/19/23

One Resistor in a Series Circuit

IR1

+VR1−

+VR2

−

IT

IR2

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.

1404/19/23

PRACTICE: Find the current IT in all the components.Find VR2, the voltage on R2.

IR1+4V−

+VR2

−

IT

IR2VS 9V

R1 = 1KΩR2 = 470Ω

R1R1

1

T R1

R2 T 2

V 4VI = = =4mA

R 1KΩ

I =I =4mA

V =I R = 4mA 470Ω =1.88V

•Ohm’s Law•Series Circuits•Ohm/s Law

1504/19/23

Generalized Series Resistor Generalized Series Resistor CircuitCircuit

1 2 2 4T nI I I I I I 1 2 3 4S nV V V V V V

But with resistors, we now have Ohm’s Law to work with also: n n nV I R

+V1− +V2− +V3− +V4− +Vn−

VS IT

I1 I2 I3 I4 In

R1 R2 R3 R4 Rn

Therefore:

S 1 2 3 4 n

S T 1 T 2 T 3 T 4 T n

S T 1 2 3 4 n

S T T

V = V +V +V +V + +V

V = I R +I R +I R +I R + +I R

V =I R +R +R +R + +R

V =I R

1604/19/23

PRACTICE: PRACTICE: Find IFind ITT

ST

T

T

T

T

VI =

R

25vI =

(82Ω+18Ω+15Ω+10Ω)

I =0.2A

I =200mA

R4

R3

R2R1

VS

10Ω

15Ω

18Ω82Ω

25v

IT

1704/19/23

How would you find the values of these How would you find the values of these unlabeled resistors?unlabeled resistors?

Assume you have a power supply, an Assume you have a power supply, an ammeter, and a voltmeter to help you.ammeter, and a voltmeter to help you.

1804/19/23

Is this what you had in mind?Is this what you had in mind?Measuring each resistor voltage and dividing by Measuring each resistor voltage and dividing by the total circuit current we can determine each the total circuit current we can determine each resistor value.resistor value.

PowerSupply 12 V

2.5v

25mA

R1 R2R3 R4

3v 4.5v 2v

1

2.5100

25

VR

mA

1904/19/23

Resistors and Resistors and Kirchhoff’s Kirchhoff’s VoltageVoltage

LawLaw

Fox Valley Technical CollegeAppleton, WI, USA

2004/19/23

Sum of Sum of nn voltage drops voltage drops equals the source voltage.equals the source voltage.

VS =

V1

V2

V3

VN

-

+

-

+

-

+

-

+

-

+

2104/19/23

Series ResistorSeries ResistorVoltage Voltage DividersDividers

Fox Valley Technical CollegeAppleton, WI, USA

2204/19/23

Two Resistor Voltage DividerTwo Resistor Voltage Divider

Can we find VCan we find V11 and V and V22 without first finding Iwithout first finding ITT??

+

-

+

-

VS

V1

V2R2

R1

IT

+

-

The source voltage is applied between these two terminals.This notation is equivalent to a battery symbol.

X X

S T

XSX

T

V RV R

RV V

RIn 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. 2304/19/23

Example: Two Resistor Voltage DividerExample: Two Resistor Voltage Divider

2

100 210 10 6.67

150 3

RV v v

1

50 110 10 3.33

150 3

RV v v

10v

100Ω

50Ω+

-RT=150Ω

R1

R2

2404/19/23

A Multiple Resistor Voltage DividerA Multiple Resistor Voltage Divider(The same formula still applies.)

VS

V1

V2

V3

V4

V5

R1

R2

R3

R4

R5

I

+

-

+-+-+-+-+-

X

SXT

RV V

R2504/19/23

The The PotentiometerPotentiometeras a Voltage as a Voltage

DividerDivider

Fox Valley Technical CollegeAppleton, WI, USA

2604/19/23

The Potentiometer as a Voltage DividerThe Potentiometer as a Voltage Divider

Potentiometer

3

2

1

1

2

3VS

+

-

1

2

3VS

+

-

2704/19/23

Adjusting the Voltage DividerAdjusting the Voltage Divider

5.0vVS

+

-

1

2

3

10v

9.5v

VS

+

-

1

2

3

10v

2.0vVS

+

-

1

2

3

10v

2804/19/23

A voltage divider used for volume controlA voltage divider used for volume control

AudioAmplifier

IFAmplifier Detector

VolumeControl

2904/19/23

The Voltage DividerThe Voltage Divideras a Voltage Referenceas a Voltage Reference

VoltageDivider

R1

R2

VS

There is a lower voltage at this pointwhich can be used as a voltage referencefor another circuit.

It cannot be used as a power source however.

3004/19/23