• Author / Uploaded
• Gabriel Carl Alpuerto

Citation preview

Module 1 Fundamental Principles in DC Circuits

Engr. Gerard Ang School of EECE

RESISTANCE Electric Resistance (R) – it is the property of a material that limits the amount of flow of current and converts electric energy to heat energy. Its unit is the Ohm (Ω) named in honor of the German Physicist Georg Simon Ohm (1787 – 1854). Factors affecting resistance: 1. Nature of the material 2. Length of the material 3. Cross-sectional area of the material 4. Temperature

Where: R = resistance of the material A = cross-sectional area of the material ρ = resistivity or specific resistance of the material L = length of the material V = volume of the material Resistivity – it is the resistance offered to a current if passed between the opposite faces of a unit cube of the material. It is measured in ohm-m.

Sample Problems 1. A coil consists of 2,000 turns of copper wire having a cross-sectional area of 0.8 mm2. The mean length per turn is 80 cm and the resistivity of copper is 0.02 μΩ-m. Find the resistance of the coil. Solution:

Sample Problems 2. A heater element is made of nichrome wire having resistivity equal to 100 x 10-8 Ω-m. The diameter of the wire is 0.4 mm. Calculate the length of the wire required to get a resistance of 40 Ω. Solution:

Sample Problems 3. The resistance of a conductor 1 mm2 in cross-section and 20 m long is 0.346 Ω. Determine the specific resistance of the conductor material. Solution:

Sample Problems 4. A wire of length 1 m has a resistance of 2 Ω. Obtain the resistance if specific resistance is doubled, diameter is doubled and the length is made three times of the first. Solution:

Dividing eq. (2) by (1)

Sample Problems 5. Determine the resistivity of the material of conductor of volume 0.05 m3, length 300 meters and resistance 0.0306 Ω. Solution:

Sample Problems 6. One km of wire having a diameter of 11.7 mm and of resistance 0.031 Ω is drawn so that its diameter is 5 mm. What does its resistance become? Solution:

Dividing eq. (2) by (1)

Sample Problems 7. Find the resistance of a cubic centimeter of copper (a) when it is drawn into a wire of diameter 0.032 mm and (b) when it is hammered into a flat sheet of 1.2 mm thickness, the current flowing through the sheet from one face to another, specific resistance of copper is 1.6 x 10-8 Ω-m. Solution:

(a) When it is drawn into a wire of diameter 0.032 mm

(b) When it is hammered into a flat sheet of 1.2 mm thickness

CIRCULAR MILS AND SQUARE MILS Circular mil (CM) – it is the area of a circle whose diameter is one mil. 1,000 mils = 1 inch 1 MCM = 1,000 CM Where: d = diameter of the conductor in mils

Square mil – it is the area of a square whose side is one mil.

EFFECT OF TEMPERATURE IN RESISTANCE The effect of variations of temperature on the resistance of all materials is generally are as follows: • Resistance of most of the metallic conductors usually increases with rise in temperature. • Resistance of non-conductors or insulator usually decreases with rise in temperature. Where: R2 = resistance at temperature t2, Ω R1 = resistance at temperature t1, Ω t1 = initial temperature, °C t2 = final temperature, °C T = inferred zero resistance, °C = temperature when resistance of a certain material is zero α = temperature coefficient of resistance, /°C = increase in resistance per ohm per °C rise in temperature α0 = temperature coefficient of resistance at 0°C

Sample Problems 1. A copper conductor has its specific resistance of 1.6 x 10-6 ohm-cm at 0°C and a resistance temperature coefficient of 1/254.5 per °C at 20°C. Find (a) the specific resistance and (b) the resistance temperature coefficient at 60°C. Solution: (a) For the specific resistance at 60°C

(b) For the resistance temperature coefficient at 60°C

Sample Problems 2.

Two coils connected in series have resistances of 600 Ω and 300 Ω with temperature coefficient of 0.1% and 0.4% respectively at 20°C. (a) Find the resistance of the combination at a temperature of 50°C. (b) What is the effective temperature coefficient of the combination? Solution: (a) For the resistance of the combination at a temperature of 50°C

Sample Problems Solution: (b) For the effective temperature coefficient of the combination

Sample Problems 3.

Two materials A and B have resistance temperature coefficients of 0.004 and 0.0004 respectively at a given temperature. In what proportion must A and B be joined in series to produce a circuit having a temperature coefficient of 0.001? Solution:

Sample Problems 4.

A coil has a resistance of 18 Ω when its mean temperature is 20°C and of 20 Ω when its mean temperature is 50°C. Find its mean temperature rise when its resistance is 21 Ω and the surrounding temperature is 15°C. Solution:

Sample Problems Dividing eq. (2) by eq. (1)

Dividing eq. (3) by eq. (1)

Sample Problems 5.

A semi-circular ring of copper has an inner radius of 6 cm, radial thickness 3 cm and an axial thickness 4 cm. Find the resistance of the ring at 50°C between its two end-faces. Assume specific resistance of Cu at 20°C = 1.724 x 10-6 ohm-cm and resistance-temperature coefficient of Cu at 0°C = 0.0043/°C.

Solution:

Sample Problems Solution:

CONDUCTANCE • Conductance (G) – it is the measure of the ease with which electric current will flow through a material. It is the reciprocal of resistance. Its unit is Siemens (S) named after two German engineers, Werner and William Siemens (19th century).

Where:

σ = conductivity of the material

RESISTORS • Resistor – it is any device, which exhibits solely the property of resistance. A resistor can either be linear or non-linear. • Classification of Resistors: 1. Fixed resistance type 2. Variable resistance type • Types of resistors: 1. Carbon composition resistors 2. Wire-wound resistors 3. Metal film resistors 4. Carbon film resistors 5. Cermet film resistor • Power Rating or Wattage Rating – it is the maximum power the resistor can dissipate without being damaged without overheating. Typical power rating of resistors are 1/8, ¼, ½, 1, 2 and 5 watts. 1. The larger the physical size of a resistor, higher is the power rating. 2. Higher wattage resistors can operate at higher temperatures 3. Wire-wound resistors are physical larger with wattage rating than carbon resistors.

Schematic Symbols for Various Resistors

RESISTOR COLOR CODING Resistor color-coding is used due to the small physical size of the resistor to determine the resistance and tolerance value of a carbon resistor. Usually, these resistors are provided with four-color bands, which are printed at the insulated body of the resistor.

Tolerance Value – it is the amount, in percent, by which the actual (measured) resistance value can deviate from the color-coded resistance value.

1st Digit

2nd digit

Multiplier

Tolerance

Black

-

0

100

-

Brown

1

1

101

±1%

Red

2

2

102

±2%

Orange

3

3

103

-

Yellow

4

4

104

-

Green

5

5

105

-

Blue

6

6

106

-

Violet

7

7

107

-

Gray

8

8

108

-

White

9

9

109

-

Gold

-

-

10-1

±5%

Silver

-

-

10-2

±10%

No color

-

-

Color

±20%

Resistor Color Coding Exercises 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

red-red-black-silver blue-gray-black-gold brown-green-brown-gold orange-orange-brown-silver green-blue-brown –gold brown-red-red–silver red-violet-red–silver gray-red-red–gold brown-black-orange–gold orange-orange-orange–silver blue-gray-yellow–none green-black-green-silver

Resistor Color Coding Exercises 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

27 @ 10% 56 @ 10% 180 @ 5% 390 @ 10% 680 @ 5% 1.5 k @ 20% 3.6 k @ 10% 7.5 k @ 5% 10 k @ 5% 47 k @ 10% 820 k @ 10% 2.2 M @ 20 %