Lecture 2 Resistance Ohm’s Law Electric Energy Electric Power Efficiency

Lecture 2

• Resistance• Ohm’s Law• Electric Energy • Electric Power• Efficiency

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• The common units: Volts, Amps, Ohms, Coulombs are all named after people

Volta Ampere Ohm Coulomb

Resistance

• The resistance of a conductor is due to the collisions between free electrons and atoms.

• When the same voltage is applied across different conductors, different currents flow.

• Some conductors offer more opposition or resistance to the passage of current than others.

Factors Affecting Resistance

1. The length L of the material. Longer materials have greater resistance.

1 W

L

2 W

2L

If the wire doubles in length, it doubles in resistance

2. The cross-sectional area A of the material. Larger areas offer LESS

resistance.

. • Notice that the electrons

seem to be moving at the same speed in each one but there are many more electrons in the larger wire.

• This results in a larger current which leads us to say that the resistance is less in a wire with a larger cross sectional area.

It can be shown thatR1/A.

• For metals and a lot of insulators, when temperature is raised, the lattice ions vibrate more vigorously, increasing the frequency of collision between electrons and the lattice. The resistance therefore increases.  T ↑ R↑⇒

3. The higher temperatures result in higher resistances.

4. The kind of material. Iron has more electrical resistance than a geometrically similar copper conductor.

Ig < Is < IcR glass > R steel > R copper

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TYPES OF RESISTORS (Fixed and variable) Fixed Resistors

FIG. 3.13 Fixed-composition resistors: (a) construction; (b) appearance.

Calculating Resistance

• It’s possible to calculate resistance of a resistor using the color bands on it– AB represent a 2 digit number– C represents the magnitude

– Resistance = AB * 10C + D

Example: Calculating Resistance

• The first two bands correspond to 4 and 7. The third band tells you the number of zeros following.

47*103 = 47,000 Ω + 10%

Larger devices have a larger surface area.

A physically larger device is able to dissipate more heat and handle more power.

11

Since a device loses heat through its surface, the larger the surface area, the more heat a device dissipates. Heat dissipation is related to

device surface area.

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Variable Resistors -- Potentiometers

• is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider.

Rac = Rab + Rbc

Construction

Setting the Value of Resistance

EGR 101 14

RheostatsA variable resistance used to control current

Usually a two-terminal variable resistorPotentiometer can be wired as a rheostat

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TEMPERATURE EFFECTS

Demonstrating the effect of a positive temperature coefficient( a-for conductors) and a negative temperature coefficient (b-for semiconductors )on the resistance

Temperature Coefficient

For most materials, the resistance R changes in

proportion to the initial resistance Ro and to the

change in temperature Dt.

0R R t Change in resistance:

The temperature coefficient of resistance, a

is the change in resistance per unit resistance per unit degree change of temperature.

00

1; Units:

C

R

R t

Example : The resistance of a copper wire is 4 mW at 200C. What will be its resistance if heated to 800C? Assume that a = 0.004 /Co.

0 00 ; (0.004 / C )(4 m )(60 C )R R t R

Ro = 4 m ; W Dt = 80oC – 20oC = 60 Co

DR = 1.03 mWDR = 1.03 mW

R = Ro + DR

R = 4 mW + 1.03 mW

R = 5.03 mWR = 5.03 mW

Resistivity of a materialis a measure of how strongly a material opposes the flow of electric current

is called the resistivity of the material.

AR

1 As R and

AR

get We

AR

Hence

The unit of is .m

1 •Conductivity of material , s

Resistivity of various materials

Material Class (.m )

Copper Good conductor 1.72 10-8

Aluminum Good conductor 2.65 10-8

Germanium Semiconductor 0.6

Silicon Semiconductor 2300

Quartz insulator 5 1016

Ohm’s Law Every conversion of energy from one form to

another can be related to this equation.

In electric circuits the effect we are trying to establish is the flow of charge, or current.

The potential difference, or voltage between two points is the cause (“pressure”),

The resistance is the opposition encountered.

Ohm’s Law Developed in 1827 by Georg Simon Ohm

For a fixed resistance, the greater the voltage (or pressure) across a resistor, the more the current.

The more the resistance for the same voltage, the less the current.

Current is proportional to the applied voltage and inversely proportional to the resistance.

Ohm’s Law (Golden Triangle)

; ; V V

I V IR RR I

Plotting Ohm’s Law

Plotting Ohm’s Law

Insert Fig 4.8

Example : When a 3-V battery is connected to a light, a current of 6 mA is observed. What is the resistance of the light filament?

Source of EMF

RI

+ -

V = 3 V6 mA

3.0 V

0.006 A

VR

I

R = 500 WR = 500 W

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In this first example, we will calculate the amount of current (I) in

a circuit, given values of voltage (E) and resistance (R):

What is the amount of current (I) in this circuit?

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In the last example, we will calculate the amount of voltage supplied by a

battery, given values of current (I) and resistance (R):

What is the amount of voltage provided by the battery?

Energy

Energy (W ) lost or gained by any system is determined by:

W = P×t

Since power is measured in watts (or joules per second) and time in seconds, the unit of energy is the wattsecond (Ws) or joule (J)

Power Power is an indication of how much work (the

conversion of energy from one form to another) can be done in a specific amount of time; that is, a rate of doing work.

• Power is the rate of doing work– Power = Work / time

• Power is measured in watts (W)• Work and energy measured in joules (J)• One watt = One joule per second

Power in Electrical Systems

• From V = W /Q → W = V × Q• and I = Q / t → Q = I× t • W = V× I × t , P = W / t• P = V× I × t / t → P = V× I • From Ohm’s Law ( I = V / R ), we can

also find that

P = I 2 R and P = V 2 / R

32

Power in Electrical Systems

• We should be able to use any of the power equations to solve for V, I, or R if P is given

• For example:

PRV

R

PI

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WATT’S LAW ( Magic Circle )

Efficiency Efficiency () of a system is determined by the

following equation:

= Po / Pi

Where: = efficiency , (η is Greek letter eta) Po = power output

Pi = power input

- Poor efficiency in energy transfers results in wasted energy , generates more heat .

- Heat must be removed (requires fans and heat sinks)

Efficiency

• To find the total efficiency of a system–Obtain product of individual efficiencies

of all subsystems:

Total = 1 × 2 × 3 × ∙∙∙

EfficiencyThe basic components of a generating (voltage) system

are depicted below, each component has an associated efficiency, resulting in a loss of power through each stage.

Insert Fig 4.19