oracabessa high school€¦ · web view2020/04/01 · fusible resistors this type is a wire-wound...

2.8 - The principles of Resistancea. Definition of resistance.b. Types of resistors:

i. carbon film;ii. metal film;

iii. wire wound;iv. SMD;v. VDR; and,

vi. LDR.c. Identifying resistor values form colour code for carbon resistors.d. Drawing and connecting total resistance in series, parallel and

series/parallel.e. Calculating total resistance in series, parallel and series-parallel

circuits.f. Calculating total conductance of resistance in parallel.g. Using circuit diagrams to show current flows.h. Calculating resistivity values:

i. (i) defining resistivity;ii. (ii) calculating conductor resistance for changes in length and

cross-sectional area;iii. (iii) known factors (value, area, length); and,iv. (iv) equivalent resistance of series resistance.

i. Temperature coefficient of resistance:i. change in material resistance produced by change in

temperature:o positive temperature coefficient;o negative temperature coefficient; and,o zero temperature coefficients.

ii. identifying materials with positive, negative and zero temperature coefficients; and,

iii. solving problems involving resistivity and temperature co-efficient of resistance.

2.8 The principles of Resistance

January 8, 2020

Define Resistor and ResistanceResistance is the opposition to flow of current in a circuit.Resistor is a component which offers opposition to the flow of current in a circuit.

1) Define the following:a. Resistance (2 marks)b. Resistor (2 marks)

Function of a ResistorThe main function of a resistor is to reduce the current (I) to the desired value (in parallel), or to provide the desired voltage (V) in a circuit (in series).

Figure 2.20 – Carbon resistors

2) State the two (2) functions of a resistor (2 marks)

Type of ResistorsThere are three main categories of resistors:

1) fixed resistor: a resistor with a value that does not change example 6Ω.

2) variable resistor: is a resistor with changing value example 0 – 10kΩ.

3) special resistor: a resistor that is use for a specific purpose example Voltage Dependent Resistor (VDR).

3) List the three (3) categories of resistors and explain any one. (5 marks)

Type of Fixed ResistorsThe two main characteristics of a resistor are its resistance R in ohms and its power rating W in watts. There are five (5) types of fixed resistor:

Wire-Wound Resistors A wire wound resistor is a resistor which use a special type of wire called resistance wire is wrapped around an insulating core (porcelain, cement, or just plain pressed paper). The length of wire and its specific resistivity determine the resistance of or the resistor.

4) Define wire wound resistor. (2 marks)

Carbon-Composition Resistors This type of resistor is made of finely divided carbon or graphite mixed with a powdered insulating material as a hinder, in the proportions needed for the desired R value. Carbon resistors are commonly available in R values of 1Ω to 20 MΩ.

5) Define carbon-composite resistor. (2 marks)

Film-Type Resistors

There are two kinds of film-type resistors: (1) Carbon- film and (2) Metal-film resistors

6) Define film-type resistor. (2 marks)

January 9, 2020

The carbon-film resistor: is made by depositing a thin layer of carbon on an insulated substrate. The carbon film is then cut in the form of a spiral to form the resistive element. The resistance value is controlled by varying the proportion of carbon to insulator.

7) Define carbon-film resistor. (2 marks)

Metal-film resistors: are constructed in a manner similar to the carbon-film type. However, in a metal-film resistor a thin film of metal is sprayed onto a ceramic substrate and then cut in the form of a spiral. The length, thickness, and width of the metal spiral determine the exact resistance value. Metal-film resistors have even more precise R values than do carbon-film resistors.

8) Define metal-film resistor. (2 marks)

Surface-mount resistorsSurface-mount resistors, also called chip resistors, are constructed by depositing a thick carbon film on a ceramic base. The exact resistance value is determined by the composition of the carbon itself, as well as by the amount of trimming done to the carbon deposit.

9) Define surface-mount resistor. (2 marks)

Fusible resistors This type is a wire-wound resistor made to burn open easily when the power rating is exceeded. It then serves the dual functions of fuse and a resistor to limit the current.

10) Define fusible resistor. (2 marks)

RESISTOR COLOR CODING

Because carbon resistors are small physically, they are colour-coded to mark their resistance value in ohms. There are four types of colour-coded resistors: (1) 1-band, (2) 3-band, (3) 4-band and (4) 5-band.

1-Band Resistor (Zero Ohms Resistor)The 1-band resistor is a resistor with a black band. This represents 0Ω because black is zero on the resistor table.

3-Band Resistor Colour CodeThe table below provides information to follow when calculating the value for three band resistors.

Example #1: A resistor has a colour code of red, blue and gold, find the value of its resistance using Table 8.1.Solution 26 x 0.1 = 2.6Ω

ExercisesCalculate the following resistor values for the following 3-Band resistors.1. Red, White & Gold2. Blue, Orange & Silver3. Green, Yellow & Gold4. Gray, Violet & Silver

TABLE 8.1 - THREE BANDS RESISTOR COLOUR CODEColours Names 1st Band

(1st digit)2nd Band (2nd digit)

3rd Band(decimal multiplier)

Black 0 0 -Brown 1 1 -Red 2 2 -Orange 3 3 -Yellow 4 4 -Green 5 5 -Blue 6 6 -Violet 7 7 -Gray 8 8 -White 9 9 -

Gold - - x 0.1Silver - - x 0.01

11) A resistor has a colour code of blue, Orange and gold, find the value of its resistance using Table.

4-Band Resistor Colour CodeTable 2.1 below provides information to follow when calculating the value for three band resistors. The first and second band on the resistor that is being calculated will be a number of value 0-9 and the third band will determine the number of zeros to be added to the first two digits and the forth band can either be silver (±10%) or gold ± 5%).

TABLE 2.2 - FOUR BANDS RESISTOR COLOUR CODEColours Names

1st Band (1st digit)

2nd Band (2nd digit)

3rd Band(decimal multiplier)

4th Band (tolerance)

Black 0 0 x 1 -Brown 1 1 x 10 -Red 2 2 x 100 -Orange 3 3 x 1,000 -Yellow 4 4 x 10,000 -Green 5 5 x 100,000 -Blue 6 6 x 1000,000 -Violet 7 7 x 10,000,000 -Gray 8 8 x 100,000,000 -White 9 9 x 1,000,000,000 -

Gold - - - ±5%Silver - - - ±10%

STOP…..

Example #1: A resistor has a colour code of red, blue, red and gold, find the value of its resistance using Table 8.2.

Solution

Red, Blue, Red and Gold2 6 00 Ω ± 5%

5% x 2600 = 130Ω

Therefore 2600Ω – 130 = 2470Ω and 2600Ω + 130 = 2730Ω

Resistor range is 2470Ω to 2730Ω

January 18, 2017

ExercisesCalculate the resistance values for the following 4-Band resistors.1. Red, White, Brown & Gold 290 [270.5 to 304.5]2. Blue, Orange, Red & Silver 6300 [5670 to 6930]3. Green, Yellow, Orange & Gold 54 000[51 300 to 56 700]4. Gray, Violet, Black & Silver 87 [78.3 to 95.7]

12) A resistor has a colour code of green, yellow, orange and gold, find the value of its resistance using Table.

5-Band Resistor Colour CodeTable 2.3 below provides information to follow when calculating the value for five band resistors. The first, second and third band on the resistor that is being calculated will be numbers each of value 0-9 and the fourth band will determine the number of zeros to be added to the 3-digits (formed from the first three bands) to complete the value of the resistor. The fifth band when calculated will give a value which must be subtracted (to get the lower value) and added (to get the upper value) in order to create a range within which the resistor is usable.

TABLE 8.3 - FIVE BAND RESISTOR COLOUR CODEColours Names

1st Band (1st digit)

2nd Band (2nd digit)

3rd Band (3rd digit)

4th Band(decimal multiplier)

5th Band (tolerance)

Black 0 0 0 x 1 -Brown 1 1 1 x 10 ±1%Red 2 2 2 x 100 ±2%Orange 3 3 3 x 1,000 -Yellow 4 4 4 x 10,000 -

Green 5 5 5 x 100,000 ±0.5%Blue 6 6 6 x 1000,000 ±0.25%Violet 7 7 7 x 10,000,000 ±0.1%Gray 8 8 8 x 100,000,000 -White 9 9 9 x

1,000,000,000-

Example #1: A resistor has a colour code of red, blue, red, yellow and red, find the value of its resistance using Table 2.3.

Solution Red [2], Blue [6], Red [2], yellow [4] & Red [±2%] = 2,620,000 ±

2%Resistance of the 5-band resistor = 2,620,000ΩValue of the tolerance (2% x 2,620,000Ω) = 52,400Ω

Lower limit (2,620,000Ω - 52,400Ω) = 2,567,600ΩUpper limit (2,620,000Ω + 52,400Ω) = 2,672,400Ω

Therefore the range for which the 5-band resistor is usable = 2,567,600Ω (lower) - 2,672,400Ω (upper)

ExercisesCalculate the following resistor values for the following 5-Band resistors.

1. Red, White, Brown, Red & Brown 29 100 ±1%2. Blue, Orange, yellow, Orange & Red 634 000 ±2%3. Green, Yellow, Blue, Orange & Green 546 000 ±0.5%4. Gray, Violet, White, Brown & Blue 8 790 ±0.25%5. Gray, Violet, Orange, yellow & Violet 8 730 000 ±0.1%

13) A resistor has a colour code of gray, violet, orange, yellow and violet, find the value of its resistance using Table.

January 24, 2017

Variable resistorThere are two types: (1) rheostat and (2) potentiometer

Rheostat: Rheostat is a device used to regulate an electric current by increasing or decreasing the resistance of the circuit. Some common uses of the rheostat are to dim lights, to control the speed of an electric motor, and to control the volume of a radio. The accompanying diagram shows a simple rheostat. Current flows into the resistance coil and from the resistance coil through the slider. When the control knob is turned, the slider moves along the coil; the amount of resistance is thus changed by varying the length of the current's path through the resistance coil.

Potentiometer: Potentiometer informally called a pot, is a three-terminal resistor with a sliding contact that forms an adjustable voltage divider. If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat.

A potentiometer measuring instrument is essentially a voltage divider used for measuring electric potential (voltage); the component is an implementation of the same principle, hence its name.

Potentiometers are commonly used to control electrical devices such as volume controls on audio equipment. Potentiometers operated by a mechanism can be used as position transducers, for example, in a joystick. Potentiometers are rarely used to directly control significant power (more than a watt), since the power dissipated in the potentiometer would be comparable to the power in the controlled load.

14) Define the following:a. Potentiometerb. Rheostat

Comparison of Rheostat and PotentiometerRheostat Potentiometer

1 How much terminals does the device have?

2 3

2 How is the device connected to the load in the circuit?

In series In parallel

3 What is the device used to control in the circuit?

Current Voltage

Special ResistorLight Dependent Resistor (Photo Resistor): A Light Dependent Resistor (LDR) or a photo resistor is a device whose resistivity is a function of the incident electromagnetic radiation. Hence, they are light sensitive devices.

January 25, 2017

Voltage-dependent resistor (VDR): it has a nonlinear, non-ohmic current–voltage characteristic that is similar to that of a diode. In contrast to a diode however, it has the same characteristic for both directions of traversing current.

15) Define the following:a. Light Dependent Resistor LDR (2 marks)b. Voltage dependent resistor VDR (2 marks)

Resistance in Series, Parallel and Combination Circuits A circuit is a path which leads current around in a loop. There are three ways in which resistors can be connected in a circuit:

(1) Series: in a series circuit resistors are connected one after the other.Series ResistanceRT = R1 + R2 …RT = 3Ω + 6ΩRT = 9Ω

16) Calculate the total resistance of two resistors 6Ω and 4Ω that are connected in series. (3 marks)

(2) Parallel: in a series circuit resistors are connected one across the other.Parallel Resistance

1 = 1 + 1RT R2 R3

1 = 1 + 1RT 3Ω 6Ω

2 + 1 = 3 6 6

1 = 3RT 6

RT = 6 Ω or 2Ω 3

17) Calculate the total resistance of two resistors 6Ω and 4Ω that are connected in parallel. (4 marks)

(3) Combination: in a combination circuit resistors are connected part in parallel and part in series.

Combination Resistance(1) Solve the parallel part

1 = 1 + 1RT R2 R3

1 = 1 + 1RT 4Ω 6Ω 3 + 2 = 5 12 121 = 5RT 12RT = 12 Ω or 2.4Ω 5

(2) Solve the series partRT = R1 + R2,3

RT = 3Ω + 2.4ΩRT = 5.4Ω

18) Calculate the total resistance in the circuit below. (5 marks)

Conductance Conductance is the degree to which an object conducts electricity, calculated as the ratio of the current which flows to the potential difference present. This is the reciprocal of the resistance, and is measured in Siemens (S). The symbol of conductance is G.

G = 1 R

Conductance in series and parallel circuitConductance in series is similar to resistance in parallel and conductance in parallel is similar to resistance in series. The formulae are as follow:

Conductance in series1 = 1 + 1 + 1GT G1 G2 G3 ...

Conductance in parallelGT = G1 + G2 + G3 ...

19) What is conductance? (2 marks)20) What is the unit and symbol of conductance? (2 marks)21) What is the formula for calculating conductance in parallel? (2 marks)

Effect of Heat on a ConductorWhen current pass through a conductor the temperature rises example, an element. The resistance of pure metals, such as copper and aluminium, increases as temperature increases (positive temperature coefficient). The resistance of certain alloy remain relatively constant as temperature increases (constant temperature coefficient). But the resistance of carbon and electrolyte decrease as temperature increases (negative temperature coefficient).

Temperature Coefficient is the increase in resistance of a piece of material measuring 1Ω when its temperature increases by 1 0C. The symbol for temperature coefficient is α (Greek letter alpha) and the unit is Ω/Ω 0C. Temperature coefficient of copper is 0.004 Ω/Ω 0C.

22) What is temperature coefficient? (2 marks)23) What is the unit and symbol of temperature coefficient? (2 marks)

Calculate Resistance IncreaseThere are two formulae for calculating the increase in resistance:

(1)Temperature increase from 00CRf = R0 (1 + αt)

Where R0 = resistance at 00C, Rf = final resistance, α = temperature coefficient and t = temperature

Example: The resistance of a coil wire at 00C is 100Ω. Calculate the resistance of the coil at 300C. α = 0.004Ω/Ω deg C.Rf = R0 (1 + αt)

Rf = ?R0 = 100Ωα = 0.004Ω/Ω 0Ct = 300C

Rf = R0 (1 + αt)Rf = 100 (1 + 0.004 x 30)

Rf = 100 (1 + 0.12)Rf = 100 (1.12)Rf = 112Ω

Exercises: a) The resistance of a coil wire at 00C is 200Ω. Calculate the resistance of

the coil at 450C. α = 0.004Ω/Ω deg C.b) The resistance of a coil wire at 00C is 150Ω. Calculate the resistance of

the coil at 250C. α = 0.004Ω/Ω deg C.c) The resistance of a coil wire at 00C is 300Ω. Calculate the resistance of

the coil at 500C. α = 0.004Ω/Ω deg C.d) The resistance of a coil wire at 00C is 375Ω. Calculate the resistance of

the coil at 370C. α = 0.004Ω/Ω deg C.e) The resistance of a coil wire at 00C is 425Ω. Calculate the resistance of

the coil at 420C. α = 0.004Ω/Ω deg C.

24) The resistance of a coil wire at 00C is 375Ω. Calculate the resistance of the coil at 370C. α = 0.004 Ω/Ω deg C. (5 marks)

February 7, 2017

(2) Temperature increase between two temperaturesR2 = 1 + αt2

R1 1 + αt1

Where R1 = 1st resistance, R2 = 2nd resistance, α = temperature coefficient, t1

= 1st temperature and t2 = 2nd temperature

Example: the field coil of a motor has a resistance of 200Ω at 200C. Find the resistance of the coil when the motor temperature increases to 400C. α = 0.004Ω/Ω 0C.

R1 = 200 ΩR2 = ?t1 = 20 0Ct2 = 40 0C

α = 0.004 Ω/Ω 0C

R2 = 1 + αt2

R1 1 + αt1

R2 = 1 + 0.004Ω/Ω0C x 400C200Ω 1 + 0.004Ω/Ω0C x 200C

R2 = 1 + 0.16200 1 + 0.08

R2 = 1.16200 1.08

R2 x 1.08 = 1.16 x 200

R2 x 1.08 = 2321.08 1.08

R2 = 214.81Ω

Exercises1. The field coil of a motor has a resistance of 100Ω at 150C. Find the

resistance of the coil when the motor temperature increases to 250C. α = 0.004Ω/Ω 0C.

2. The field coil of a motor has a resistance of 150Ω at 300C. Find the resistance of the coil when the motor temperature increases to 450C. α = 0.004Ω/Ω 0C.



25) The field coil of a motor has a resistance of 150Ω at 300C. Find the resistance of the coil when the motor temperature increases to 450C. α = 0.004 Ω/Ω 0C. (5 marks)

Resistance of a conductorThere are four (4) factors which affects resistance: (1) length, (2) cross-sectional area, (3) type of material and (4) temperatureLength: if the length of the conductor is doubled then the resistance will doubledCross-sectional Area: if the cross-sectional area is doubled the resistance will be halved.Type of material: if the type of material is different then the resistance will vary based on the specific resistance of the each material.Temperature: temperature changes affect the resistance of a material (see above).

February 8, 2017 Resistivity or specific resistance: is the resistance of a unit cube of a material measured across the opposite faces. The unit of resistivity is µΩ-cm and the symbol is ρ (Greek letter rho).

R = ρl a

R = resistance, ρ = resistivity (specific resistance), l = length and a = cross-sectional area

26) What is resistivity? (2 marks)27) What is the unit and symbol for resistivity? (2 marks)

Example #1: Calculate the resistance of a copper cable 1000 meters long if it has a cross-sectional area of 50mm2. The resistivity of copper is 1.7µΩ-cm.

R = ?l = 1000 mρ = 1.7µΩ-cma = 50mm2

R = ρl aR = 1.7µΩ-cm x 1000 m 50mm2

R = 0.0000017 Ω-cm x 100, 000 cm 0.5 cm2

R = 0.17 Ω-cm 2 0.5 cm2

R = 0.34 Ω

Exercises 1. Calculate the resistance of a copper cable 500 meters long if it has a

cross-sectional area of 10mm2. The resistivity of copper is 1.7µΩ-cm.

2. Calculate the resistance of a copper cable 2000 meters long if it has a cross-sectional area of 16mm2. The resistivity of copper is 1.7µΩ-cm.



Convert 1 000 m to cm1 000 x 100 = 100 000 cm

Convert 50 mm2 to cm2

50/100 = 0.5 cm2

1.7µΩ-cm to Ω-cm0.0000017 Ω-cm

28) Calculate the resistance of a copper cable 100 meters long if it has a cross-sectional area of 25mm2. The resistivity of copper is 1.7µΩ-cm. (5 marks)

Example #2: A PVC twin copper cable 50m long has a total voltage drop of 8V when it is carrying a current of 40A. Calculate the cross-sectional area of the cable and the power loss in the cable when this current is flowing.

Find R of the cable using the voltage drop (V) and current carried by the cable (I)

R = V R = 8V R = 0.2 Ω I 40 A

Since R = ρl Then a = ρl a R

l = 50 mR = 0.2 Ωρ = 1.7 µΩ-cma = ?

a = ρl R

a = 1.7 x 10 -6 Ω-cm x 50m 0.2Ω

a = 0.0000017 Ω-cm x 10 000 cm 0.2Ω

a = 0.017 Ω-cm 2 0.2Ω

a = 0.085 cm2

Convert 0.085 cm2 to mm2 (multiply by 100)

Convert twin 50 m to cm (2 x 50) x 100 = 10 000 cm

Convert 1.7 µΩ-cm to Ω-cm0.0000017 Ω-cm

0.085 cm2 x 100 = 8.5 mm2 (To the nearest cable size 10 mm2)

Calculate power loss of the cablePower loss = I2RPower loss = 40A x 40A x 0.2ΩPower loss = 320W

ExercisesComplete the following:1. A PVC twin copper cable 80m long has a total voltage drop of 6V when it

is carrying a current of 50A. Calculate the cross-sectional area of the cable and the power loss in the cable when this current is flowing.

2. A PVC twin copper cable 30m long has a total voltage drop of 4V when it is carrying a current of 20A. Calculate the cross-sectional area of the cable and the power loss in the cable when this current is flowing.



Example #3: Calculate the smallest cross-sectional area of a PVC twin copper cable that can be used to supply 240V, 50A to a guardhouse 100 m away from the main supply point.

Find the voltage drop of the cableMaximum allowable voltage drop of any cable is 2.5% of the supply voltage.

2.5 x 240 V = 6 V100

Find the resistance of the cable using voltage drop and currentR (of cable) = voltage drop Current

R (of cable) = 6 V 50 A

R (of cable) = 0.12 Ω

Find cross-sectional area of the cablel = 100 m (twin cable)R = 0.2 Ωρ = 1.7 µΩ-cma = ?

Since R = ρl Then a = ρl a R

a = 1.7 x 10 -6 Ω-cm x 100 m (twin cable) 0.12 Ω

a = 0.0000017 Ω-cm x 20 000 cm 0.12 Ω

a = 0.034 Ω-cm 2 0.12 Ω

a = 0.034 Ω-cm 2 0.12 Ω

a = 0.2833 cm2

Convert 0.2833 cm2 to mm2 (multiply by 100)0.2833 cm2 x 100 = 28.33 mm2 (The nearest cable size is 35mm2)

Exercise: 1. Calculate the smallest cross-sectional area of a PVC twin copper cable

that can be used to supply 120V, 50A to a guardhouse 50m away from the main supply point.

Convert twin 100 m to cm (2 x 100) x 100 = 20 000 cm

Convert 1.7 µΩ-cm to Ω-cm0.0000017 Ω-cm

2. Calculate the smallest cross-sectional area of a PVC twin copper cable that can be used to supply 240V, 80A to a guardhouse 200m away from the main supply point.



oracabessa high school€¦ · web view2020/04/01 · fusible resistors this type is a wire-wound...

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