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Chapter 2 – Resistive Circuits

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Chapter 2 – Resistive Circuits. Objectives: to learn about resistance and Ohm’s Law to learn how to apply Kirchhoff’s laws to resistive circuits to learn how to analyze circuits with series and/or parallel connections to learn how to analyze circuits that have wye or delta connections. - PowerPoint PPT Presentation
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Fall 2001 ENGR201 Circuits I - Chap ter 2 1 Chapter 2 – Resistive Circuits Read pages 14 – 50 Homework Problems - TBA Objectives: to learn about resistance and Ohm’s Law to learn how to apply Kirchhoff’s laws to resistive circuits to learn how to analyze circuits with series and/or parallel connections to learn how to analyze circuits that have wye or delta connections
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Page 1: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 1

Chapter 2 – Resistive Circuits

• Read pages 14 – 50• Homework Problems - TBA

Objectives:• to learn about resistance and Ohm’s Law• to learn how to apply Kirchhoff’s laws to resistive

circuits• to learn how to analyze circuits with series and/or

parallel connections• to learn how to analyze circuits that have wye or

delta connections

Page 2: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 2

Resistance - Definition

• Resistance is an intrinsic property of matter and is a measure of how much a device impedes the flow of current.

• The greater the resistance of an object, the smaller the amount of current that will flow for a given applied voltage.

• The resistance of an object depends on the material used to construct the object (copper has less resistance than plastic), the geometry of the object (size and shape), and the temperature of the object. (R = L/A)

Page 3: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 3

Resistance – Applications

• Sometimes we want to minimize the resistance of an object (in a conductor, for instance).

• Sometimes we want to maximize the resistance (in an insulator).

• Sometimes we to relate the resistance of the object to some physical parameter (such as a photoresistor or RTD).

• Sometimes we want to precisely control the resistance of an element in order to influence the behavior of a circuit such as an amplifier.

Page 4: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 4

Resistance - Sizing

Resistors come in all shapes and sizes (see Figure 2.1 in your text). However, several common parameters are used to characterize resistors: 

ohmic value (nominal) measured in Ohms (), maximum power rating measured in Watts

(W), and precision (or tolerance) measured as a

percentage of the ohmic value.

Page 5: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 5

Ohm’s Law - describes the relationship between the current through and the voltage across a resistor.

Different devices connected to a power source demand different amounts of power from that source. That is, different devices present differing amounts of loading.

The 6w bulb offers more resistance to the flow of current than the 12w bulb.

I = 0.5A I = 1A

12V12V 6W 12W

Ohm’s Law

Page 6: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 6

• Rather than specify the load that a device represents in terms of its voltage/power rating, we can specify that load in terms of its resistance.

• The smaller the resistance the greater the load (the greater the power demand).

Ohm’s Law – Mathematical Definition

R = V/II = V/R V = IR

+V-

R I

I = 0.5A I = 1A

12V12V 6W 12W

R = 12V/0.5A = 24 R = 12V1A = 12

Page 7: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 7

How much current will a 12V/12W lamp demand if 6V is applied to it? How much power is demanded?

6V12V 12W 12W

Example

A 12w/12v lamp will draw 1A of current:• P = VI 12W = 12V I I = 1A• V = IR (Ohm’s Law) R = 12V/1A = 12• Therefore, if V = 6V I = 6V/1A = 12 • P = 6v 0.5A = 3W = 0.25 12W. • Since both the voltage and current are halved, the

power is cut by a factor of four.

Page 8: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 8

R is the resistance of the device, measured in ohms (). The greater the value of R, the smaller the value of I.

R = V/I +V-

I = 0A

12V

Open Circuit, R = I = 0 regardless of the value of V (NO LOAD)

(air, plastic, wood)

Short & Open Circuits

Short Circuit, R =0V = 0 regardless of thevalue of I

(wire)

I =

12V V

Page 9: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 9

• Ohms’ law relates the magnitude of the voltage with the magnitude of the current AND

• the polarity of the voltage to the direction of the current.

Resistors always absorb power, so resistor current always flows through a voltage drop.

+V-

I = V/RR

Ohm’s Law – Voltage Polarity & Current Direction

Page 10: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 10

Ohms’ Law can be represented graphically – called a VI characteristic:

+V-

R I = V/R

I

V

m = Slope = V/I = R

Ideal resistor, VI characteristic

Ohm’s Law - Graphically

Page 11: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 11

V

I

Short circuit, slope = 0 (V = 0)

Open circuit, slope = (I = 0)

V

I

Practical resistor VI characteristic

Pmax

Pmax

Non-ideal Resistors

Page 12: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 12

• Resistance is a measure of how much a device impedes the flow of current. Conductance is a measure of how little a device impedes the flow of current.

• Resistance and conductance are simply two different ways to describe the voltage-current characteristic of a device.

• At times, especially in electronic circuits, it is advantageous to work in terms of conductance rather than resistance

Conductance

Page 13: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 13

Resistance: R = V/I, (ohms)

+V-

Conductance:G = I/V, S(seimens)

+V-

(G = 1/R = R-1)

Conductance - Units

Old style symbol for conductanceOld style units = mho

Page 14: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 14

P = VI (any device)for a resistor:P = V(V/R) = V2/RorP = (IR)I = I2R

P = VI (any device)In terms of conductance:P = V(VG) = V2GorP = (I/G)I = I2/G

Resistance: R

+V-

I

V = IR = I/G

Resistance – Power Equations

P = VIP = V2/RP = I2R

Page 15: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 15

Kirchhoff’s Laws• Kirchhoff’s Current Law (KCL)• Kirchhoff’s Voltage Law (KVL)

A node is a “point” in a circuit where two or elements are connected.

RR R+

-

Node-A

Kirchhoff’s Laws

RR R

Node-A

+-

Page 16: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 16

Kirchhoff’s Current Law

• The algebraic sum of all currents at any node in a circuit is exactly zero.

• The sum of all currents entering = sum of all currents leaving

• We neither gain nor lose current at a node.

I1

I2 I3R

R R+-

Node-A

I4

I1-I2+I3-I4 = 0

I1+I3 = I2+I4

KCL

Page 17: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 17

Kirchhoff’s Voltage Law (KVL)

A loop is a closed path about a circuit that begins and ends at the same node. However, no element may be traversed more than once.

A

B C D

E

Five loops in the circuit shown are:

A-C-B-A

A-D-C-A C-D-E-C

B-C-E-B

A-D-E-B-AAre there more loops ?

KVL

Page 18: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 18

• The algebraic sum of all voltages about any loop in a circuit is exactly zero.

• The sum of all increases (rises) = sum of all voltage decreases (drops)

• We do not gain or lose voltage if we start and end at the same node.

A

BC D

E

+ V1 -

- V2 +

+ V3

-

+ V4-+

V5 -

+ Vx -+ V6-

+ Vy-

By KVL:• V2 + V3 - V1 = 0• -V3 + V4 - Vx = 0• V1 + Vy - V6 = 0• Vx + V5 -Vy = 0• V2 + V4 + V5 - V6 = 0

KVL

Page 19: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 19

Two circuits are equivalent if, for any source connected to the circuits, they demand the same amount power. The two circuits “look” the same to the source

I1

+

-Vs

Device

#1

P1 = VSI1

I2

+

-Vs

Device

#2

P2 = VSI2

P1 = P2 VSI1 = VSI2 I1 = I2

If the applied voltage is the same, two equivalent circuits will demand the same amount of current from the source.

EquivalentCircuits

Page 20: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 20

Rab

a

b

a

b

R1

R4

R3R2

R6 R5

Rab

Series connection (all elements have the same current)

a

b

R1

R4

R3R2

R6 R5

VabI Vab

I

Rab

Vab = I Rab

Series Resistance

Page 21: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 21

By KCL: IR1 = IR2 = … = IR6 = IBy KVL: Vab = IR1+ IR2+ IR3+ IR4+ IR5+ IR6Vab/I = (R1 + R2 + R3 + R4 + R5 + R6) = Rab

a

b

R1

R4

R3R2

R6 R5

VabI Vab

I

Ra

b

Vab = I Rab

The equivalent resistance of two or more series-connected resistors is the sum of the individual resistors.

Series Resistance

Page 22: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 22

Parallel connection (all the elements have the same voltage)

Vab/I = Rab

Parallel Resistance

Vab

I

Rab

Vab

I

R1 R2 R3 R4 R5

A

B

by KCL:I = I1 + I2 + I3 + I4 + I5I = Vab/R1 + Vab/R2 + Vab/R3 + Vab/R4 + Vab/R5I = Vab[R1-1 + R2-1 + R3-1 + R4-1 + R5-1 ]Vab/I = [R1-1 + R2-1 + R3-1 + R4-1 + R5-1 ]-1

Page 23: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 23

Vab

I

Rab

Vab

I

R1 R2 R3 R4 R5

Vab/I = Rab

Rab = [R1-1 + R2-1 + R3-1 + R4-1 + R4-1 ]-1

Since G = 1/R = R-1

Rab = [G1 + G2 + G3 + G4 + G5]-1

Gab = G1 + G2 + G3 + G4 + G5

Parallel Resistance

Page 24: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 24

The total voltage applied to a group of series-connected resistors will be divided among the resistors. The fraction of the total voltage across any single resistor depends on what fraction that resistor is of the total resistance.

a

b

R1

R4

R3R2

R6 R5

VabI

RTOTAL = Rab = R1 + R2 + R3 + R4 + R5 + R6

+V4

-

4

4

1 2 3 4 5 6ab

RV V

R R R R R R

The Voltage Divider Rule (VDR)

Page 25: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 25

The total current applied to a group of resistors connected in parallel will be divided among the resistors. The fraction of the total current through any single resistor depends on what fraction that resistor is of the total conductance.

GTOTAL = R1-1 + R2 -1 + R3 -1 + R4 -1 + R5 -1

1

5 1 1 1 1 1

5 5

1 2 3 4 5Total TotalTotal

G RI I I

G R R R R R

I5

VabR1 R2 R3 R4 R5

ITotal

The Current Divider Rule (CDR)

Page 26: Chapter 2 – Resistive Circuits

Fall 2001 ENGR201 Circuits I - Chapter 2 26

For two resistors:1

2

1 2Total

RI I

R R

Itotal = I1 + I2

R1 R2I1

I2

2

1

1 2Total

RI I

R R

CDR – Two Resistors

Observations:• The smaller resistor will have the larger current.• If R1= R2, then I1 = I2

• If R1 = nR2, then I2 = nI1


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