Current, Voltage and Resistance

ENTC 210: Circuit Analysis I

Rohit SinghalLecturerTexas A&M University

Administrative Tasks

Fix Exam Schedule Lab details

TA – Mr. Pankaj BhagawatSections Merge

Atoms and their structure

electron

neutron

proton

Atomic Structure

Mass of an Electron = 9.11 x 10-28 gm. Mass of a Proton = 1.672 x 10-24 gm. Proton is ~1836 times heavier than the

electron

Atomic Structure

Unit of Charge = Coulombs Charge on electron = charge on a proton =

1.6 x 10-19 C 1 Coulomb = Charge on 6.242 x 1018

electrons

Coulomb’s Law

Like charges repel, opposites attractF = k Q1 Q2 / r2

k = 9 x 109 (units?)

Coulomb’s Law

Like charges repel, opposites attractF = k Q1 Q2 / r2

K = 9 x 109 N m2/C2

Conduction

In metals, the electrons are “more free” than the insulators.

Whenever there is a charge present at one end, the electrons flow to (or away) from that charge.

Current

Rate of flow of charge 1 Amp = 1 Coulomb / 1 Second.

Question

If a laptop needs constantly needs 2 Amps current from a battery, how many electrons are drained from the battery in one hour?

1 Amp = 6.242 x 1018 electrons/second 2 Amp = 12.484 x 1018 electrons/second In one hour - > 3600 x 12.484 x 1018 electrons Answer is 4.49 x 1022 electrons

Question

What’s the weight of all those electrons? 4.49 x 1022 x 9.11 x 10-28 gm 4.09 x 10-5 gm

Equations

I = Q/t Q = I x t t = Q/I

Potential

Every particle of mass m raised to a height h above the earth’s surface has a potential energy m.g.h

This potential energy can be raised by raising the particle a little higher

When the particle is set free, it travels to the point of least potential.

Electric Potential

Similarly, a charge wants to travel to a lower “electric” potential.

A negative charge on the other hand, wants to travel to a higher potential.

Each point in a circuit has a potential.

Voltage

Voltage is always measured between two points.

It is defined as the difference of potential between the two points.

Measured in volts

Volts

1 volt is defined as the potential difference, which results in an energy exchange of 1 Joule due to the movement of 1 Coulomb across it.

DC Voltage Supply

Conductivity

Copper is the most popular conductor.

Metal Conductivity (%)

Silver 105

Copper 100

Gold 70.5

Aluminum 61

Tungsten 31.2

Nickel 22.1

Iron 14

Constantan 3.52

Nichrome 1.73

Calorite 1.44

Resistance

Resistance is proportional to lengthlength

direction of current flow

Resistance

Resistance is inversely proportional to the cross sectional area

direction of current flow

Resistance

R = ρ L/A ρ is the resistivity of

the material (units?)

Material ρ (10-8 Ohm-Metres)

Silver 1.645

Copper 1.723

Gold 2.443

Aluminum 2.825

Tungsten 5.485

Nickel 7.811

Iron 12.299

Tantalum 15.54

Nichrome 99.72

Tin Oxide 250

Carbon 3500

American Wire Gage (AWG) sizes

AWG # Diameter (in) Ω /1000ft.0000 0.46 0.0490

000 0.409 0.0618

0 0.325 0.0983

1 0.289 0.1240

2 0.257 0.1563

4 0.204 0.2485

10 0.102 0.9989

14 0.0640 2.525

28 0.0126 64.90

Color Coding

5 Bands of code (3 are mandatory) Bands 1 - 3 the value of the resistor Band 4 the range (tolerance) Band 5 the reliability

Color Code (Band 1-3)

Color Value

Black 0

Brown 1

Red 2

Orange 3

Yellow 4

Green 5

Blue 6

Violet 7

Gray 8

White 9

Example

2 6 x 103 = 26 K Ohms

Band 3 (special cases)

Gold = 0.1Red Blue Gold = 2.6 Ohm

Silver = 0.01Red Blue Silver = 0.26 Ohm

More BandsBand 4 Tolerance

Gold 5%

Silver 10%

None 20%

Band 5 Reliability (after 1000 Hrs of use)

Brown 1%

Red 0.1%

Orange 0.01%

Yellow 0.001%

Example

= 26 K Ohms ± 5%, 1 in 100,000 fails after 1000 hrs of use