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Resistance and Electrical Properties, Study notes of Electrical Circuit Analysis

A comprehensive overview of the concept of resistance, including its definition, unit, factors affecting resistance, and related electrical properties. It covers topics such as ohm's law, resistor color codes, and various types of resistors like potentiometers, rheostats, varistors, and thermistors. The document also introduces the concepts of capacitance, inductance, and their associated devices, as well as the principles of electromagnetic induction. It delves into the mathematical relationships and formulas governing these electrical phenomena, making it a valuable resource for students and professionals in the field of electrical engineering and physics.

Typology: Study notes

2022/2023

Available from 08/15/2024

kaydenn
kaydenn 🇵🇭

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RESISTANCE
The property of a material to oppose or limit the flow of
current or charge
Unit: Ohms
Reciprocal: Conductance in Siemens (S) or mho
The higher the number (AWG#), the thinner the wire, the
higher the resistance
Factors Affecting Resistance
Type of material
Length of material
Cross-sectional area of the material
Temperature
𝑅2
𝑅1=(𝐿2
𝐿1)2=(𝐴1
𝐴2)2=(𝑑1
𝑑2)4
Hard Drawn Copper @ 20
𝜌=1.77×10−8 Ω m= 10.5 ΩCM
𝑓𝑡
Aluminum @ 20
𝜌=2.83×10−8 Ω m= 17.1 ΩCM
𝑓𝑡
Annealed Copper @ 20
𝜌=1.72×10−8 Ω m= 10.37 ΩCM
𝑓𝑡
CM = Circular Mill (area)
1 in = 1000 mils
Temperature Resistance Effects
HDC
Al
Annealed Copper
T = -242
T = -236
T = -234.5
Ohm’s Law
Georg Simon Ohm
Henry Cavendish (first to discover)
Resistor Color Chart
Color
1st/2nd
Band
Multiplier
Tolerance
Black
0
100
Brown
1
101
±1%
Red
2
102
±2%
Orange
3
103
Yellow
4
104
Green
5
105
±0.05%
Blue
6
106
±0.10%
Violet
7
107
±0.25%
Grey
8
108
±0.05%
White
9
109
Gold
10-1
±5%
Silver
10-2
±10%
None
±20%
Bad Boy Rape Our Young Girl But Violeta Gave Willingly
Gary Said No!!
Resistor Variations
Potentiometer (Variable resistor)
Has three connections, two fixed and one moveable
Tunable; used as knobs to control the volume of a stereo
Constructed like a resistor, but has sliding tap contact
Used as voltage dividers
Has wide range of values, limited current-handling
capability
𝑅=𝜌𝐿
𝐴=𝜌 𝑉
𝐴2=𝜌𝐿2
𝑉
𝐴=𝑑2 (𝐶𝑀)
𝐴=𝜋
4𝑑2 (𝑠𝑞 𝑚𝑖𝑙𝑠)
𝑅2=𝑅1[1+∝1(𝑡2𝑡1)]
1=1
|𝑇|+𝑡1=1
1
0+𝑡1
𝐼=𝑉
𝑅
pf3
pf4

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RESISTANCE

The property of a material to oppose or limit the flow of

current or charge

Unit : Ohms

Reciprocal : Conductance in Siemens (S) or mho

The higher the number (AWG#), the thinner the wire, the

higher the resistance

Factors Affecting Resistance

✓ Type of material

✓ Length of material

✓ Cross-sectional area of the material

✓ Temperature

2

1

2

1

2

1

2

2

1

2

4

Hard Drawn Copper @ 20 ℃

𝜌 = 1. 77 × 10

− 8

Ω − m = 10. 5

Ω − CM

Aluminum @ 20 ℃

𝜌 = 2. 83 × 10

− 8

Ω − m = 17. 1

Ω − CM

Annealed Copper @ 20 ℃

𝜌 = 1. 72 × 10

− 8

Ω − m = 10. 37

Ω − CM

CM = Circular Mill (area)

1 in = 1000 mils

Temperature Resistance Effects

HDC Al Annealed Copper

T = - 242 ℃ T = - 236 ℃ T = - 234.5 ℃

Ohm’s Law

Georg Simon Ohm

Henry Cavendish (first to discover)

Resistor Color Chart

Color 1

st

nd

Band

Multiplier Tolerance

Black

0

Brown

1

±1% F

Red

2

±2% G

Orange

3

Yellow

4

Green

5

Blue

6

Violet

7

Grey

8

White

9

Gold

  • 1

±5% J

Silver

  • 2

±10% K

None

±20% M

Bad Boy Rape Our Young Girl But Violeta Gave Willingly

Gary Said No!!

Resistor Variations

Potentiometer (Variable resistor)

 Has three connections, two fixed and one moveable

 Tunable; used as knobs to control the volume of a stereo

 Constructed like a resistor, but has sliding tap contact

 Used as voltage dividers

 Has wide range of values, limited current-handling

capability

2

2

2

2

2

1

[

1

2

1

)]

1

1

0

1

Rheostat

 Has two connections, one fixed and other moveable

 Variation of potentiometer with a high current rating

 Has limited range of values

Varistors

Voltage-sensitive resistor

Thermistor

Temperature-sensitive resistor

Resistance decreases as the temperature rises

Used in fire alarms

Light Dependent Resistor (LDR)

Changes values depending on the amount of light shining on

its surface

Resistance decreases as the amount of light increases

Conductance and Conductivity

CAPACITANCE

 Measure of the amount of electric charge stored for a

given electric potential

 Stores energy in the form of electrostatic field

 Opposes the change in voltage

Unit : Farad (F)

Reciprocal : Elastance – Daraf (F

  • 1

Capacitor

Device that stores energy in the electric field created

between a pair of conductors

Simple Capacitor :

Two copper plates separated by an air gap or a sheet of mica

Air is low cost – the best reason why air is used as a dielectric

Operation of a Capacitor

Factors Affecting Capacitance

✓ Area of the plates

✓ Distance between the plates

✓ Dielectric material

Parallel-Plate Capacitor

For n plates

Work

Point Charge/Steady Charge – no ½ as capacitor is not

constant

Multiplier

Numerator: source 𝑅

𝑆

: Series Resistance

Denominator: volt meter reading 𝑅

𝐼

: Instrument Resistance

Series: Volt meter; Parallel: Ammeter I I

= load current

Mass Charge

Electron 9.11 x 10

  • 31

kg - 1.602 x 10

  • 19

Proton 1.67 x 10

  • 27

kg - 1.602 x 10

  • 19

Neutron 1.67 x 10

  • 27

kg none

INDUCTANCE

 Name given to the property of a circuit whereby there is an

emf induced into the circuit by the change of flux linkages

produced by a current change

 Opposes the change in current

 Classified according to core type: ferromagnetic or air

Unit : Henry

Inductor

Device that stores energy in the form of magnetic field

𝐶 =

𝜀

𝑜

𝜀

𝑟

𝐴

𝑑

𝐶 =

( 𝑛 − 1

)

𝜀

𝑜

𝜀

𝑟

𝐴

𝑑

𝐶 =

𝜀

𝑜

𝐴

𝑑

𝜀

𝑟

1

𝑑

𝜀

𝑟

2

𝑑

𝜀

𝑟

3

𝑊 =

1

2

𝐶𝑉

2

=

1

2

𝑄

2

𝐶

=

1

2

𝑄𝑉

𝑀 =

𝑉

𝑆

𝑉

𝑉

=

𝑅

𝑆

𝑅

𝐼

  • 1

𝑀 =

𝐼

𝐼

𝐼

=

𝑅

𝐼

𝑅

𝑆𝐻

  • 1

(nasa ilalim ang hinahanap)

d x

For equilateral triangle with equal charges

Or

Use free body diagram (one reference axis)

2

1

1

2

𝑅

𝑅

1

1

2

2