Chapter 26[1].Elect

7/27/2019 Chapter 26[1].Elect.

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Chapter 26. Current and Resistance26.1. What is Physics?26.2. Electric Current26.3. Current Density26.4. Resistance and Resistivity26.5. Ohm's Law26.6. A Microscopic View of Ohm's Law26.7. Power in Electric Circuits

26.8. Semiconductors26.9. Superconductors


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What is Physics?


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Electric Current

The electric current is the amount ofcharge per unit time that passesthrough a plane that pass completelythrough the conductor.

The SI unit for current is a coulomb per second (C/s), called as an

ampere(A)


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Current is a Scalar


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Direction of current

A current arrow is drawn inthe direction in which positivecharge carriers would move,even if the actual chargecarriers are negative andmove in the opposite

direction.

The direction of conventionalcurrent is always from a pointof higher potential toward apoint of lower potentialthat

is, from the positive towardthe negative terminal.


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Current Density J

Current density is to study the flow ofcharge through a cross section of theconductor at a particular point

It is a vector which has the same

direction as the velocity of the movingcharges if they are positive and theopposite direction if they are negative.

The magnitude of Jis equal to thecurrent per unit area through that areaelement.


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Drift Speed

When a conductor does not have a current through it,

its conduction electrons move randomly, with no netmotion in any direction. When the conductor doeshave a current through it, these electrons actuallystill move randomly, but now they tend to driftwitha drift speedvd in the direction opposite that of the

applied electric field that causes the current

Here the product ne, whose SI unit is the coulomb

per cubic meter (C/m3), is the carrier charge density


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Sample Problem 26-3

What is the drift speed of the conductionelectrons in a copper wire with radius r=900m when it has a uniform current i=17 mA?Assume that each copper atom contributesone conduction electron to the current andthat the current density is uniform across

the wire's cross section. Mass density ofcopper is =8.96x103 kg/m3 .


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The resistance

The resis tance (R)is defined as the ratio

of the voltage Vapplied across a piece of

material to the current Ithrough the

material: R=V/i.

SI Unit o f Resistance:volt/ampere

(V/A)=ohm()


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The resistance of a conductor depends on the

manner in which the potential difference isapplied to it

Ra > Rb


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Resistivity

The unit of is ohm-meter(m):

Resistivity of a material is:

The conductivity of a material is


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The resistivity is an inherent property of thematerial

The resistivity of a material depends ontemperature. = 0[1 + (T - T0)]The term has the unit of reciprocaltemperature and is the temperature

coefficient of resistivity.

Resistivity


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. . . . . . . . Table 20.1 Resistivitiesa of Various Materials

Material Resistivity r (Wm) Material Resistivity r (Wm)

Conductors SemiconductorsAluminum 108 Carbon 105

Copper 108 Germanium 0.5bc

Gold 108 Silicon 202300bc

Iron 108

I nsulators

Mercury 108 Mica 10111015

Nichrome (alloy) 108 Rubber (hard) 10131016

Silver 108 Teflon 1016

Tungsten 108 Wood (maple) 1010

aThe values pertain to temperatures near 20 C.

bDepending on purity.

cDepending on purity.


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Calculating Resistance from Resistivity

Resistance is a property of an object. It may varydepending on the geometry of the material.

Resistivity is a property of a material.


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Checkpoint

The figure here shows three cylindrical copperconductors along with their face areas and lengths.Rank them according to the current through them,greatest first, when the same potential difference V

is placed across their lengths.


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Sample Problem

A rectangular block of iron has dimensions1.2cmx1.2cmx15cm . A potential difference is to beapplied to the block between parallel sides and insuch a way that those sides are equipotential

surfaces (as in Fig. b). What is the resistance of theblock if the two parallel sides are (1) the squareends (with dimensions ) 1.2cmx1.2cm and (2) tworectangular sides (with dimensions 1.2cmx15cm )?


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Ohm's Law

Ohm's law is an assertionthat the current through adevice is alwaysdirectly

proportional to thepotential differenceapplied to the device.

V

RI


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Power in Electric Circuits

The amount of charge dqthat movesfrom terminals a to b in time interval dtis equal to idt.

Its electric potential energy decreases inmagnitude by the amount

The decrease in electric potentialenergy from ato bis accompanied by atransfer of energy to some other form.

The power Passociated with thattransfer is the rate of transferd U/dt, which is

The unit of power


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the transfer of electricpotential

energy to thermal energy

The rate of electrical energy dissipation due to aresistance is

Caution:P=iV applies to electrical energy transfers of all kinds;P=i2R and P=V2/R apply only to the transfer of electric potential

energy to thermal energy in a device with resistance.


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Sample Problem

A copper wire of cross-sectional areaand length 4.00 m has a current of 2.00 A uniformlydistributed across that area. (a) What is themagnitude of the electric field along the wire? (b)

How much electrical energy is transferred to thermalenergy in 30 min?


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Semiconductors

Property Copper Silicon

Type of material Metal Semiconductor

Charge carrier density, m3

Resistivity,

Temperature coefficient ofresistivity, K1


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Superconductors

The resistivity of material absolutely disappears atvery low temperatures. This phenomenon ofsuperconductivity


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Conceptual Questions1. When an incandescent light bulb is turned on, the

tungsten filament becomes white hot. The

temperature coefficient of resistivity for tungsten isa positive number. What happens to the powerdelivered to the bulb as the filament heats up? Doesthe power increase, remain the same, or decrease?Justify your answer.

2. Two materials have different resistivities. Two wiresof the same length are made, one from each of thematerials. Is it possible for each wire to have thesame resistance? Explain.

3. One electrical appliance operates with a voltage of120 V, while another operates with 240 V. Based onthis information alone, is it correct to say that thesecond appliance uses more power than the first?Give your reasoning.


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4. Two light bulbs are designed for use at 120 V andare rated at 75 W and 150 W. Which light bulb hasthe greater filament resistance? Why?

5. Often, the instructions for an electrical appliancedo not state how many watts of power the applianceuses. Instead, a statement such as 10 A, 120 V isgiven. Explain why this statement is equivalent to

telling you the power consumption.

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Chapter 26[1].Elect