Electric Current

Chapter 27. Current and Chapter 27. Current and ResistanceResistance

A PowerPoint Presentation by

Paul E. Tippens, Professor of Physics

Southern Polytechnic State University

A PowerPoint Presentation byA PowerPoint Presentation by

Paul E. Tippens, Professor of PhysicsPaul E. Tippens, Professor of Physics

Southern Polytechnic State UniversitySouthern Polytechnic State University© 2007

Objectives: Objectives: After completing this After completing this module, you should be able to:module, you should be able to:

•• Define Define electric currentelectric current and and electromotive electromotive forceforce..

•• Write and apply Write and apply OhmOhm’’s laws law to circuits to circuits containing resistance and emf.containing resistance and emf.

•• Define Define resistivity resistivity of a material and apply of a material and apply formulas for its calculation.formulas for its calculation.

•• Define and apply the concept of Define and apply the concept of temperature coefficient of resistancetemperature coefficient of resistance..

Electric CurrentElectric CurrentElectric currentElectric current I I is the rate of is the rate of the flow of charge the flow of charge QQ through through a crossa cross--section section A A in a unit of in a unit of time time tt..

QIt

1C1 A1 s

One ampere A is charge flowing at the rate of one coulomb per second. One One ampereampere AA is charge flowing at is charge flowing at the rate of one the rate of one coulomb per secondcoulomb per second..

AA++

--WireWire

+Q+Q

tt

Example 1.Example 1. The electric current in a The electric current in a wire is 6 A. How many electrons flow wire is 6 A. How many electrons flow past a given point in a time of 3 s?past a given point in a time of 3 s?

I = 6 AI = 6 A; qI q It

t

qq = (6 A)(3 s) = 18 C= (6 A)(3 s) = 18 C

Recall that: 1 eRecall that: 1 e-- = 1.6 x 10= 1.6 x 10--1919 C, then convert:C, then convert:

-

20-19

1e18 C 18 C 1,125 x 10 electrons1.6 x 10 C

In 3 s: 1.12 x 1020 electrons

Conventional CurrentConventional CurrentImagine a charged capacitor with Imagine a charged capacitor with Q = CVQ = CV that is that is

allowed to discharge.allowed to discharge.

Electron flow:Electron flow: The direction The direction of eof e-- flowing from flowing from –– to +. to +.

Conventional current:Conventional current: The motion of +q from The motion of +q from + to + to –– has same effect.has same effect.

Electric fieldsElectric fields and and potentialpotential are defined in terms are defined in terms of of +q+q, so we will assume , so we will assume conventional current conventional current (even if electron flow may be the actual flow).(even if electron flow may be the actual flow).

++

--

+ -Electron

flow

+ -+ -

e-

Conventional flow

+

Electromotive ForceElectromotive ForceA A source of electromotive force (emf)source of electromotive force (emf) is a is a device that uses chemical, mechanical or device that uses chemical, mechanical or other energy to provide the potential other energy to provide the potential difference necessary for electric current.difference necessary for electric current.

Power linesPower lines BatteryBattery Wind generatorWind generator

Water Analogy to EMFWater Analogy to EMFLow

pressure

PumpWater

High pressure

ValveWater Flow

Constriction

Source of EMF

ResistorHigh potential

Low potential

Switch

E

RI

+ -

The The source of emfsource of emf (pump) provides the (pump) provides the voltagevoltage (pressure) to force (pressure) to force electronselectrons (water) through (water) through electric electric resistanceresistance (narrow constriction).(narrow constriction).

Electrical Circuit SymbolsElectrical Circuit Symbols

Electrical circuitsElectrical circuits often contain one or more often contain one or more resistors grouped together and attached to resistors grouped together and attached to an energy source, such as a battery.an energy source, such as a battery.

The following symbols are often used:The following symbols are often used:

+ - + -- + - + -

Ground Battery-+

Resistor

Electric ResistanceElectric ResistanceSuppose we apply a constant potential difference Suppose we apply a constant potential difference of of 4 V4 V to the ends of geometrically similar rods to the ends of geometrically similar rods of, say: steel, copper, and glass.of, say: steel, copper, and glass.

4 V 4 V 4 V

Steel Copper Glass

Is Ic Ig

The current in glass is much less than for The current in glass is much less than for steel or iron, suggesting a property of steel or iron, suggesting a property of materials called materials called electrical resistance R.electrical resistance R.

OhmOhm’’s Laws LawOhmOhm’’s laws law states that the current states that the current II through a through a given conductor is directly proportional to the given conductor is directly proportional to the potential difference potential difference VV between its end points.between its end points.

OhmOhm’’s law allows us to define s law allows us to define resistance Rresistance R and to write the following forms of the law:and to write the following forms of the law:

' :Ohm s law I V

; ; V VI V IR RR I

Example 2. Example 2. When a When a 33--VV battery is battery is connected to a light, a current of connected to a light, a current of 6 mA6 mA is observed. What is the resistance of is observed. What is the resistance of the light filament?the light filament?

Source of EMF

RI

+ -

V = 3 V6 mA

3.0 V0.006 A

VRI

R = 500 RR = 500 = 500

The The SI unitSI unit for electrical for electrical resistance is the resistance is the ohmohm, ,

1 V1 1 A

AmmeterAmmeterVoltmeterVoltmeter RheostatRheostatSource of Source of EMFEMF

Rheostat

A

Laboratory Circuit SymbolsLaboratory Circuit Symbols

V Emf-

+

Factors Affecting ResistanceFactors Affecting Resistance1. The 1. The length Llength L of the material. Longer of the material. Longer

materials have greater resistance.materials have greater resistance.

1 1

LL

2 2

2L2L

2. The cross2. The cross--sectional sectional area Aarea A of the material. of the material. Larger areas offer Larger areas offer LESSLESS resistance.resistance.

2 2 AA

1 1

2A2A

Factors Affecting R (Cont.)Factors Affecting R (Cont.)3. The 3. The temperature Ttemperature T of the material. The of the material. The

higher temperatures usually result in higher temperatures usually result in higherhigher resistances.resistances.

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

RRoo

R > RR > Roo

RRii > > RRccCopperCopper IronIron

Resistivity of a MaterialResistivity of a MaterialThe The resistivity resistivity is a property of a material is a property of a material that determines its electrical resistance that determines its electrical resistance RR..

Recalling that Recalling that RR is directly proportional is directly proportional to length to length LL and inversely proportional and inversely proportional to area to area AA, we may write:, we may write:

or L RARA L

The unit of resistivity is the The unit of resistivity is the ohmohm--meter (meter (

m)

Example 3.Example 3. What What lengthlength LL of copper wire is of copper wire is required to produce a required to produce a 4 4 mm

resistor? Assume resistor? Assume

the diameter of the wire is the diameter of the wire is 1 mm 1 mm and that the and that the resistivity resistivity of copper is of copper is 1.72 x 101.72 x 10--8 8 ..mm ..

2 2(0.001 m)4 4DA

AA = 7.85 x 10= 7.85 x 10--77 mm22

LRA

-7 2

-8

(0.004 )(7.85 x 10 m )1.72 x 10 m

RAL

L = 0.183 mRequired length is:Required length is:

Temperature CoefficientTemperature CoefficientFor most materials, the resistance For most materials, the resistance RR changes changes in proportion to the initial resistance in proportion to the initial resistance Ro and and to the change in temperature to the change in temperature tt..

0R R t Change in Change in resistance:resistance:

The The temperature coefficient of resistance, temperature coefficient of resistance,

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

00

1; Units:C

RR t

Example 4.Example 4. The resistance of a copper wire is The resistance of a copper wire is 4.00 4.00 mm

at at 202000CC. What will be its resistance if . What will be its resistance if

heated to heated to 808000CC? Assume that ? Assume that = 0.004 /C= 0.004 /Coo..

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

RRoo = 4.00 = 4.00 mmtt = 80= 80ooC C –– 2020ooC = 60 CC = 60 Coo

R = 1.03 mR = 1.03 m R = RR = Roo + + RR

R = R = 4.00 4.00 mm

+ 1.03 mm

R = 5.03 mR = 5.03 m

Electric PowerElectric PowerElectric powerElectric power P P is the rate at which electric is the rate at which electric energy is expended, or work per unit of time.energy is expended, or work per unit of time.

V q

V

To charge C: Work = To charge C: Work = qVqV

and Work qV qP It t t

Substitute Substitute q = It , q = It , then:then:

VItPt

P = VI

I

Calculating PowerCalculating Power

Using OhmUsing Ohm’’s law, we can find electric s law, we can find electric powerpower from any two of the following parameters: from any two of the following parameters: current current II, , voltagevoltage VV, and, and resistanceresistance RR..

OhmOhm’’s law: s law: V = IRV = IR

22; ; VP VI P I R P

R

Example 5.Example 5. A power tool is rated at A power tool is rated at 9 A9 A when used with a circuit that provides when used with a circuit that provides 120120--V.V. What power is used in operating this tool?What power is used in operating this tool?

P = VI =P = VI = (120 V)(9 A)(120 V)(9 A) P = 1080 WP = 1080 W

Example 6.Example 6. A 500A 500--W heater draws a current W heater draws a current of 10 A. What is the resistance?of 10 A. What is the resistance?

R = 5.00 R = 5.00 22 2

500 W; (10 A)

PP I R RI

Summary of FormulasSummary of Formulas

QIt

1C1 A1 s

Electric current: Electric current:

; ; V VI V IR RR I

Ohm’s LawOhm’s Law

1 voltResistance: 1 ohm1 ampere

Temperature coefficient of resistance:Temperature coefficient of resistance:

Summary (Cont.)Summary (Cont.)

or L RARA L

00

1; Units:C

RR t

22; ; VP VI P I R P

R

0R R t

Resistivity of materials:

Resistivity of Resistivity of materials:materials:

Electric Power P: Electric

Power P:

CONCLUSION: Chapter 27CONCLUSION: Chapter 27 Current and ResistanceCurrent and Resistance