Chapter 19Chapter 19

Electric CurrentsElectric Currents

Sources of Electromotive ForceSources of Electromotive Force

Devices supply electrical energy, e.g. Devices supply electrical energy, e.g. batteries, electric generatorsbatteries, electric generators

Two (or more) terminals with a Two (or more) terminals with a potential difference.potential difference.

When charge flows out from one When charge flows out from one terminal, equal charge flows into the terminal, equal charge flows into the other terminalother terminal

Electric CurrentElectric Current

Whenever electric charges of like Whenever electric charges of like signs move, an signs move, an electric currentelectric current is is said to existsaid to exist

The current is the The current is the rate at which the rate at which the charge flows through the wirecharge flows through the wire

The SI unit of current is Ampere (A)The SI unit of current is Ampere (A)• 1 A = 1 C/s1 A = 1 C/s

t

QI

ExampleExample

In a tv tube, 5 x 10In a tv tube, 5 x 101414 electrons shoot electrons shoot out in 4 s. What is the electric out in 4 s. What is the electric current? current?

Current: amount of charge flowing through a point per unit time

Current flows from higher potential to lower potential

I

= R I

Ohm’s law

R

ResistanceResistance

In a conductor, the voltage applied In a conductor, the voltage applied across the ends of the conductor is across the ends of the conductor is proportional to the current through proportional to the current through the conductorthe conductor

The constant of proportionality is the The constant of proportionality is the resistanceresistance of the conductor of the conductor

I

VR

Resistance, contResistance, cont

Units of resistance are Units of resistance are ohmsohms ( (Ω)Ω)• 1 1 Ω = 1 V / AΩ = 1 V / A

Resistance in a circuit arises due to Resistance in a circuit arises due to collisions between the electrons collisions between the electrons carrying the current with the fixed carrying the current with the fixed atoms inside the conductoratoms inside the conductor

Ohm’s LawOhm’s Law

Experiments show that for many Experiments show that for many materials, including most metals, the materials, including most metals, the resistance remains constant over a wide resistance remains constant over a wide range of applied voltages or currentsrange of applied voltages or currents

This statement has become known as This statement has become known as Ohm’s LawOhm’s Law• V = I RV = I R

Ohm’s Law is an empirical relationship Ohm’s Law is an empirical relationship that is valid only for certain materialsthat is valid only for certain materials• Materials that obey Ohm’s Law are said to be Materials that obey Ohm’s Law are said to be

ohmicohmic

ExampleExample

A 1.57 V battery connects to a light A 1.57 V battery connects to a light bulb. If the current through the bulb bulb. If the current through the bulb is 0.21 A, what is the resistance of is 0.21 A, what is the resistance of the bulb?the bulb?

V = R IResistance, R = V/I[R] = V/A = Ohm

For a fixed potential difference across a resistor,the larger R, the smaller current passing through it.

Req

Parallel connection Series connection

R1

R2

R3

R1R2 R3

Req = R1 + R2 + R3

1/Req = 1/R1+1/R2+1/R3

• Electrical wires can be bent and/or stretched.• A Node point (branching point) can be moved arbitrarily along the wire.

There are n identical resistors connected in parallel. Req?

1/Req = 1/R + 1/R + 1/R + … + 1/R = n/R

Req = R/n

Ra

Rb

(1) 1/Req = 1/Ra + 1/Rb

(2) Req is smaller than Ra and Rb

20

25

Req ≈ 10

1000 = 1k

2

Req < 2Practically all the current flowsThough the bottom one!!

Ohm’s law:Ohm’s law: = R = R·I·I

R = 6

6 V

I = /R = (6 V)/(6 Ohm) = 1.0 A

What is the electric potential at ? We cannot tell the absolute potential at this point. If at is +6 V, then 0 V at If at is +3 V, then -3 V at

For both, the potential diff. is 6 V.

To be able to specify absolute potential at a given point, we need to specify a reference point “0” potential.

GROUND

R1 = 6

6 V = “0”

Then, at is +6 V.

Electrical Energy and PowerElectrical Energy and Power

In a circuit, as a charge moves through the In a circuit, as a charge moves through the battery, the electrical potential energy of battery, the electrical potential energy of the system is increased by the system is increased by QVQV• The chemical potential energy of the battery The chemical potential energy of the battery

decreases by the same amountdecreases by the same amount As the charge moves through a resistor, it As the charge moves through a resistor, it

loses this potential energy during loses this potential energy during collisions with atoms in the resistorcollisions with atoms in the resistor• The temperature of the resistor will increaseThe temperature of the resistor will increase

Electrical Energy and Power, Electrical Energy and Power, contcont

The rate at which the energy is lost is The rate at which the energy is lost is the powerthe power

From Ohm’s Law, alternate forms of From Ohm’s Law, alternate forms of power arepower are

IVVt

QP

R

VRIP

22

Electrical Energy and Power, Electrical Energy and Power, finalfinal

The SI unit of power is Watt (W)The SI unit of power is Watt (W)• I must be in Amperes, R in ohmsI must be in Amperes, R in ohms and V and V

in Voltsin Volts The unit of energy used by electric The unit of energy used by electric

companies is the companies is the kilowatt-hourkilowatt-hour• This is defined in terms of the unit of This is defined in terms of the unit of

power and the amount of time it is power and the amount of time it is suppliedsupplied

• 1 kWh = 3.60 x 101 kWh = 3.60 x 1066 J J

ExampleExample

Light bulb 60 W, 120 V. Find Light bulb 60 W, 120 V. Find resistance of the light bulb.resistance of the light bulb.

Bulbs in seriesBulbs in series Bulbs in parallelBulbs in parallel

ResistivityResistivity

The resistance of an ohmic conductor The resistance of an ohmic conductor is proportional to its length, L, and is proportional to its length, L, and inversely proportional to its cross-inversely proportional to its cross-sectional area, Asectional area, A

• ρ is the constant of proportionality and ρ is the constant of proportionality and is called the is called the resistivityresistivity of the material of the material

A

LR

L

A

R =

Resistivity: material parameter same for any shape in a given material.

[] = .m

e.g. for copper = 1.7 x 10-8

gold = 2.44 x 10-8

tungsten = 5.6 x 10-8

iron = 9.5 x 10-8

nickel-chrome = 150 x 10-8

L /A

ExampleExample

A silver wire has a resistance of 2A silver wire has a resistance of 2. . What would be the resistance of a What would be the resistance of a silver wire twice its length and half silver wire twice its length and half its diameter?its diameter?

Temperature Variation of Temperature Variation of ResistivityResistivity

For most metals, resistivity increases For most metals, resistivity increases with increasing temperaturewith increasing temperature• With a higher temperature, the metal’s With a higher temperature, the metal’s

constituent atoms vibrate with constituent atoms vibrate with increasing amplitudeincreasing amplitude

• The electrons find it more difficult to The electrons find it more difficult to pass the atomspass the atoms

Temperature Variation of Temperature Variation of Resistance, contResistance, cont

For most metals, resistivity increases For most metals, resistivity increases approximately linearly with approximately linearly with temperature over a limited temperature over a limited temperature range, resultingtemperature range, resulting

T-TT-Too is temperature change is temperature change is the is the temperature coefficient of resistivitytemperature coefficient of resistivity RRo o is the resistance at Tis the resistance at Too

)]TT(1[RR oo

Ag: 3.8 x 103.8 x 10-3-3 /C /C

Cu: 3.9 x 103.9 x 10-3-3 /C /C Fe:5.0 5.0

x 10x 10-3-3 /C /C

ExampleExample

Light bulb (60 W; 120 V; 240 Light bulb (60 W; 120 V; 240 ) ) operates at 1800 C. What is the operates at 1800 C. What is the resistance of the filament (tungsten) resistance of the filament (tungsten) at 20 C?at 20 C?