Chapter 17Chapter 17

Current and ResistanceCurrent and Resistance

General Physics

Current, Resistance, and PowerCurrent, Resistance, and Power

Ch 17, Secs. 1–4, 6–7Ch 17, Secs. 1–4, 6–7

(skip Sec. 5)(skip Sec. 5)

General Physics

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 rate at which the charge flows through this the charge flows through this surfacesurface• Look at the charges flowing Look at the charges flowing

perpendicularly to a surface of area Aperpendicularly to a surface of area A

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

QI

t

General Physics

Electric Current, contElectric Current, cont

The direction of the current is the direction The direction of the current is the direction positive charge would flowpositive charge would flow• This is known as This is known as conventional current directionconventional current direction

In a common conductor, such as copper, the current In a common conductor, such as copper, the current is due to the motion of the negatively charged is due to the motion of the negatively charged electronselectrons

It is common to refer to a moving charge It is common to refer to a moving charge as a mobile as a mobile charge carriercharge carrier• A charge carrier can be positive or negativeA charge carrier can be positive or negative

General Physics

Current and Drift SpeedCurrent and Drift Speed

Charged particles move Charged particles move through a conductor of cross-through a conductor of cross-sectional area Asectional area A

n is the number of charge n is the number of charge carriers per unit volume carriers per unit volume (charge carrier density)(charge carrier density)

n A n A Δx is the total number of Δx is the total number of charge carrierscharge carriers

The total charge is the number The total charge is the number of carriers times the charge per of carriers times the charge per carrier, qcarrier, q• ΔΔQ = (n A Q = (n A Δx) qΔx) q

General Physics

Current and Drift Speed, contCurrent and Drift Speed, cont

The drift speed, vThe drift speed, vdd, is the speed , is the speed at which the carriers moveat which the carriers move• vvdd = = Δx/ΔtΔx/Δt

Rewritten: Rewritten: ΔΔQ = (n A Q = (n A vvdd Δt) q Δt) q So, current, I = So, current, I = ΔQ/Δt = nqvΔQ/Δt = nqvd d AA If the conductor is isolated, the If the conductor is isolated, the

electrons undergo random electrons undergo random motionmotion

When an electric field is set up in When an electric field is set up in the conductor, it creates an the conductor, it creates an electric force on the electrons electric force on the electrons and hence a currentand hence a current

General Physics

Charge Carrier Motion in a Charge Carrier Motion in a ConductorConductor

The zig-zag black line The zig-zag black line represents the motion of represents the motion of charge carrier in a charge carrier in a conductorconductor• The net drift speed is The net drift speed is

smallsmall The sharp changes in The sharp changes in

direction are due to direction are due to collisionscollisions

The net motion of The net motion of electrons is opposite the electrons is opposite the direction of the electric direction of the electric fieldfield

Active Figure: Electron Drift in a Conductor

General Physics

Electrons in a CircuitElectrons in a Circuit

The drift speed is much smaller than the The drift speed is much smaller than the average speed between collisionsaverage speed between collisions

When a circuit is completed, the electric When a circuit is completed, the electric field travels with a speed close to the field travels with a speed close to the speed of lightspeed of light

Although the drift speed is on the order of Although the drift speed is on the order of 1010-4-4 m/s the effect of the electric field is m/s the effect of the electric field is felt on the order of 10felt on the order of 1088 m/s m/s

General Physics

Meters in a Circuit – Ammeter and Meters in a Circuit – Ammeter and Voltmeter Voltmeter

An ammeter is used An ammeter is used to measure currentto measure current• In line with the bulb, In line with the bulb,

all the charge passing all the charge passing through the bulb also through the bulb also must pass through the must pass through the metermeter

A voltmeter is used A voltmeter is used to measure voltage to measure voltage (potential difference)(potential difference)• Connects to the two Connects to the two

ends of the bulbends of the bulb

General Physics

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

VR

I

General Physics

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

General Physics

Georg Simon OhmGeorg Simon Ohm

1787 – 18541787 – 1854 Formulated the Formulated the

concept of resistanceconcept of resistance Discovered the Discovered the

proportionality proportionality between current and between current and voltagesvoltages

General Physics

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• ΔV = I RΔV = 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

General Physics

Ohm’s Law, contOhm’s Law, cont

An ohmic deviceAn ohmic device The resistance is The resistance is

constant over a wide constant over a wide range of voltagesrange of voltages

The relationship The relationship between current and between current and voltage is linearvoltage is linear

The slope is related The slope is related to the resistanceto the resistance

General Physics

ResistivityResistivity

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

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

• See table 17.1See table 17.1

A

lR

General Physics

Temperature Variation of Temperature Variation of ResistanceResistance

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 increasing constituent atoms vibrate with increasing amplitudeamplitude

• The electrons find it more difficult to pass The electrons find it more difficult to pass through the atomsthrough the atoms

For most metals, resistivity increases For most metals, resistivity increases roughly linearly with temperature over roughly linearly with temperature over a limited temperature rangea limited temperature range

General Physics

SuperconductorsSuperconductors A class of materials and A class of materials and

compounds whose resistances fall compounds whose resistances fall to virtually zero below a certain to virtually zero below a certain temperature, Ttemperature, TCC

• TTCC is called the critical temperature is called the critical temperature The graph is the same as a normal The graph is the same as a normal

metal abovemetal above Once a current is set up in a Once a current is set up in a

superconductor, it persists without superconductor, it persists without any applied voltage since R = 0any applied voltage since R = 0

One application is superconducting One application is superconducting magnetsmagnets

General Physics

Electrical Energy and PowerElectrical Energy and Power In a circuit, as a charge moves In a circuit, as a charge moves

through the battery, the electrical through the battery, the electrical potential energy of the system is potential energy of the system is increased by increased by ΔQΔVΔQΔV• The chemical potential energy of The chemical potential energy of

the battery decreases by the the battery decreases by the same amountsame amount

As the charge moves through a As the charge moves through a resistor, it loses this potential resistor, it loses this potential energy during collisions with energy during collisions with atoms in the resistoratoms in the resistor• The temperature of the resistor The temperature of the resistor

will increasewill increase

General Physics

Electrical Energy and Power, contElectrical Energy and Power, cont

The rate at which energy is supplied (by source) The rate at which energy is supplied (by source) and lost (by resistance) is the powerand lost (by resistance) is the power

The SI unit of power is Watt (W)The SI unit of power is Watt (W)• 1 W = 1 VA1 W = 1 VA

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

QV I V

t

22 V

I RR

Active Figure: Ohm's Law and Electric Power

General Physics

Electrical Energy and Power, finalElectrical Energy and Power, final

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