Current and ResistanceCurrent and Resistance

A PowerPoint Presentation byA PowerPoint Presentation by

SANJAY . P CHADNAN PGT PhysicsSANJAY . P CHADNAN PGT Physics

K, V VSN NAGPURK, V VSN NAGPUR

A PowerPoint Presentation byA PowerPoint Presentation by

SANJAY . P CHADNAN PGT PhysicsSANJAY . P CHADNAN PGT Physics

K, V VSN NAGPURK, V VSN NAGPUR

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

able to:able to:• Define Define electric currentelectric current and and

electromotive forceelectromotive force..

• Write and apply Write and apply Ohm’s lawOhm’s law to circuits to circuits containing resistance and emf.containing resistance and emf.

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

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

QI

tQ

It

1C1 A

1 s

1C1 A

1 s

One One ampereampere A A is charge flowing is charge flowing at the rate of one at the rate of one coulomb per coulomb per secondsecond..

One One ampereampere A A is charge flowing is charge flowing at the rate of one at the rate of one coulomb per coulomb per secondsecond..

AA++

--WireWire

+Q+Q

tt

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

I = 6 AI = 6 A; q

I q Itt

; q

I q Itt

qq = (6 A)(3 s) = 18 = (6 A)(3 s) = 18 CCRecall that: 1 eRecall that: 1 e-- = 1.6 x 10 = 1.6 x 10-19-19 C, then C, then

convert:convert:

-20

-19

1e18 C 18 C 1,125 x 10 electrons

1.6 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 allowed to that is allowed to discharge.discharge.Electron flow:Electron flow: The The direction of edirection of e- - flowing flowing from – to +. from – to +. Conventional current:Conventional current: The motion of +q The motion of +q from + to – has same from + to – has same effect.effect.

Electric fieldsElectric fields and and potentialpotential are defined in are defined in terms of terms of +q+q, so we will assume , so we will assume conventional current conventional current (even if electron flow (even if electron flow may be the actual 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 device that uses chemical, is a device that uses chemical, mechanical or other energy to provide mechanical or other energy to provide the potential difference necessary for the potential difference necessary for electric current.electric current.

Power Power lineslines

BatteryBattery Wind Wind generatorgenerator

Water Analogy to EMFWater Analogy to EMFLow

pressure

PumpWater

High pressure

ValveWater Flow

Constriction

Source of EMF

Resistor

High 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 electric (water) through electric resistanceresistance (narrow constriction).(narrow constriction).

Electrical Circuit SymbolsElectrical Circuit Symbols

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

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

+ - + -- + - + -

Ground Battery-+

Resistor

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

4 V 4 V 4 V

Steel Copper Glass

Is Ic Ig

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

Ohm’s LawOhm’s LawOhm’s lawOhm’s law states that the current states that the current II

through a given conductor is directly through a given conductor is directly proportional to the potential difference proportional to the potential difference VV

between its end points.between its end points.

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

' :Ohm s law I V' :Ohm s law I V

; ; V V

I V IR RR I

; ; V V

I V IR RR I

Example 2. Example 2. When a When a 3-V3-V battery is battery is connected to a light, a current of connected to a light, a current of 6 6 mAmA is observed. What is the is observed. What is the resistance of the light filament?resistance of the light filament?

Source of EMF

RI

+ -

V = 3 V6 mA

3.0 V

0.006 A

VR

I

RR = 500 = 500 RR = 500 = 500

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

1 V1

1 A

1 V1

1 A

AmmeterAmmeterVoltmeterVoltmeter RheostatRheostatSource Source of EMFof EMF

Rheostat

A

Laboratory Circuit SymbolsLaboratory Circuit Symbols

V Emf-

+

Factors Affecting Factors Affecting ResistanceResistance

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

2 2 AA

1 1

22AA

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

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

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

RRoo

R > RR > Roo

RRii > R > RccCopperCopper IronIron

Resistivity of a MaterialResistivity of a Material

The The resistivity resistivity is a property of a is a property of a material that determines its electrical material that determines its electrical

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

or L RA

RA L

or L RA

RA L

The unit of resistivity is the The unit of resistivity is the ohm-meter ohm-meter ((m)

Example 3.Example 3. What What lengthlength LL of copper wire of copper wire is required to produce a is required to produce a 4 m4 m resistor? resistor? Assume the diameter of the wire is Assume the diameter of the wire is 1 1 mm mm and that the resistivity and that the resistivity of copper is of copper is 1.72 x 101.72 x 10-8 -8 ..mm ..

2 2(0.001 m)

4 4

DA

AA = 7.85 x 10 = 7.85 x 10-7-7 m m22

LR

AL

RA

-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 in proportion to the initial changes in proportion to the initial resistance resistance Ro and to the change in and to the change in temperature temperature tt..

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

The The temperature coefficient of temperature coefficient of resistance, resistance, is the change in resistance is the change in resistance per unit resistance per unit degree per unit resistance per unit degree change of temperature.change of temperature.

00

1; Units:

C

R

R t

00

1; Units:

C

R

R t

Example 4.Example 4. The resistance of a copper The resistance of a copper wire is wire is 4.00 m4.00 m at at 202000CC. What will be its . What will be its resistance if heated to resistance if heated to 808000CC? Assume ? Assume that that = 0.004 /C= 0.004 /Coo..

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

RRoo = 4.00 m = 4.00 mt = 80t = 80ooC – 20C – 20ooC = C = 60 C60 Coo

R = 1.03 mR = 1.03 m

R = RR = Roo + + RR

R = R = 4.00 m4.00 m + 1.03 mm

R = 5.03 mR = 5.03 m

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

V q

V

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

and Work qV q

P It t t

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

Pt

P = VI

I

Calculating PowerCalculating Power

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

Ohm’s law: Ohm’s law: V = IRV = IR

22; ;

VP VI P I R P

R

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 120-V.120-V. What power is used in operating What power is used in operating this tool?this tool?

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

P = 1080 W

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

R = 5.00 R = 5.00 22 2

500 W;

(10 A)

PP I R R

I

Summary of FormulasSummary of Formulas

QI

tQ

It

1C1 A

1 s

1C1 A

1 sElectric

current:Electric current:

; ; V V

I V IR RR I

; ; V V

I V IR RR I

Ohm’s LawOhm’s Law

1 voltResistance: 1 ohm

1 ampere

1 voltResistance: 1 ohm

1 ampere

Temperature coefficient of resistance:

Temperature coefficient of resistance:

Summary (Cont.)Summary (Cont.)

or L RA

RA L

or L RA

RA L

00

1; Units:

C

R

R t

00

1; Units:

C

R

R t

22; ;

VP VI P I R P

R

22; ;

VP VI P I R P

R

0R R t

Resistivity Resistivity of of

materials:materials:

Resistivity Resistivity of of

materials:materials:

Electric Power P:Electric Power P:

Check for UnderstandingCheck for Understanding

• What is voltage? What is voltage?

• How is voltage generated? (3 ways)How is voltage generated? (3 ways)

• What is current?What is current?