Chapter 19Chapter 19

Current Current and and

ResistanceResistance

19.1 Electric Current19.1 Electric Current

ObjectivesObjectives1.1. Describe the basic properties of electric Describe the basic properties of electric

currentcurrent2.2. Solve problems relating current, charge Solve problems relating current, charge

and timeand time3.3. Distinguish between the drift speed of a Distinguish between the drift speed of a

charge carrier and the average speed of the charge carrier and the average speed of the charge carrier between collisionscharge carrier between collisions

4.4. Differentiate between direct current and Differentiate between direct current and alternating currentalternating current

Where is electric current?Where is electric current?

…….wherever there is a net movement of .wherever there is a net movement of electric charge through a medium.electric charge through a medium.

ExamplesExamples

In any electronic deviceIn any electronic device

In our car enginesIn our car engines

In our bodyIn our body

What is electric current?What is electric current?

……the rate at which electric charges the rate at which electric charges move through a given areamove through a given area

Equation for Electric Current (I)Equation for Electric Current (I)

I = ΔQΔt

electric current = charge passing through a given area time interval

units of current = ampere (A)

1A = 1 C/s

Current Example ProblemCurrent Example Problem

The amount of charge that passes through the filament of a light bulb in 2.00s is 1.67C.a)What is the current in the light bulb?b)How many electrons pass through the filament in the 2.00s time span?

a) I=0.835 Ab) N = 1.04x1019 electrons

““Conventional Current” FlowConventional Current” Flow

…is defined in terms of positive charge movement

Charge MovementCharge Movement

Requires a good conductorRequires a good conductor

Examples of good conductors?Examples of good conductors? Copper and other metalsCopper and other metals Salt water and other electrolytesSalt water and other electrolytes

Electron Motion in a Conductor

When you flip on a light switch, you introduce an E-field that travels throughthe wire at nearly the speed of light(3.0x108 m/s).

But the electrons themselves do not actually travel that fast….instead they travelat a rate called the “drift velocity”.

Electrons collide with the metal atoms as they flow through the conductor, so they don’t follow a straight path

Notice direction of electron flow !!!

Drift VelocityDrift Velocity

Is the Is the net velocitynet velocity of the charge carrier of the charge carrier moving in an electric fieldmoving in an electric field

Because there are so many collisions Because there are so many collisions as the electrons move in the electric as the electrons move in the electric field, drift velocity is very small, even field, drift velocity is very small, even though E is moving VERY fast (about though E is moving VERY fast (about the speed of light)the speed of light)

Where does current come from??Where does current come from??Create a condition of unequal potential Create a condition of unequal potential energy across a conductorenergy across a conductorThe The currentcurrent flows from higher electric flows from higher electric potential (and PE) to lower electric potential (and PE) to lower electric potential (and PE)potential (and PE)

Sources of CurrentSources of Current

BatteriesBatteries: convert : convert chemicalchemical energy into energy into electrical energyelectrical energy

GeneratorsGenerators : convert : convert mechanical mechanical energy into electrical energyenergy into electrical energy

When will the current stop moving?

Types of CurrentTypes of Current

Direct current (DC)Direct current (DC) – charges move only one – charges move only one direction because the terminals of the charge direction because the terminals of the charge source always maintain the same sign (example: source always maintain the same sign (example: current flowing in a battery circuit)current flowing in a battery circuit)

Alternating current (AC)Alternating current (AC) – charges move in – charges move in both directions because the terminals of the both directions because the terminals of the charge source are constantly changing signs. charge source are constantly changing signs. There is no There is no net net motion of charge, they just motion of charge, they just vibrate back and forth (example: current in your vibrate back and forth (example: current in your house)house)

DC: constant voltage

AC: voltage flip flopsbetween + and -

time

QuestionsQuestions1.1. A 3.0 C charge passes through the filament of a light A 3.0 C charge passes through the filament of a light

bulb in 5.00 s. bulb in 5.00 s.

a) What is the current?a) What is the current?

b) How many electrons pass thru the bulb in 1.0 min?b) How many electrons pass thru the bulb in 1.0 min?

a) 0.60 A a) 0.60 A

b) 2.25x10b) 2.25x102020 electrons electrons

2.2. The compressor on an air conditioner draws 40.0 A The compressor on an air conditioner draws 40.0 A when it starts up. If the start-up time is 0.5 s, how when it starts up. If the start-up time is 0.5 s, how much charge passes in that time?much charge passes in that time?

ans: 20 Cans: 20 C

19.2 Resistance19.2 Resistance

ObjectivesObjectives1.1. Calculate the resistance, current and Calculate the resistance, current and

potential difference using the definition potential difference using the definition of resistanceof resistance

2.2. Distinguish between ohmic and non-Distinguish between ohmic and non-ohmic materialsohmic materials

3.3. Know what factors affect resistanceKnow what factors affect resistance4.4. Describe what is unique about Describe what is unique about

superconductorssuperconductors

What is resistance?What is resistance?

…….the impedance of motion of charge .the impedance of motion of charge through a conductor.through a conductor.

Which battery can provide more current to a light bulb, a 9V or a 12V?

All things being equal, the 12V battery would provide more current. But the current provided to the bulb by the battery also depends on the connecting wires and the bulb’s filament etc.

These other features in the circuit that impede current flow comprise the circuit’s resistance.

The resistance to current flow is:

R = ΔV I

Resistance = potential difference current

units of resistance = ohms (Ω)

Ohm’s LawOhm’s LawThe resistance is constant over a wide The resistance is constant over a wide range of potential differences (for most range of potential differences (for most materials)materials)

In equation form, Ohm’s Law is:In equation form, Ohm’s Law is:

ΔΔVV = constant (R) = constant (R) II

In other words: In other words: ΔΔV = IRV = IR

More on Ohm’s LawMore on Ohm’s Law

It is NOT a fundamental law of natureIt is NOT a fundamental law of nature

It is NOT true for all materialsIt is NOT true for all materials

OhmicOhmic materials do follow Ohm’s Law materials do follow Ohm’s Law and have a constant resistance over a and have a constant resistance over a wide range of wide range of ΔΔV’sV’s

Non-ohmicNon-ohmic materials are those whose materials are those whose resistance can vary over a range of resistance can vary over a range of

ΔΔV’sV’s

Ohmic materials* ΔV vs I is straight line graph* Slope of graph = I/ΔV = 1/R

Non-ohmic materials* ΔV vs I is not linear

A material’s resistance depends on:A material’s resistance depends on:

1.1. Length:Length: the longer the item, the greater it’s the longer the item, the greater it’s resistanceresistance

2.2. Cross-sectional area:Cross-sectional area: small cross sections small cross sections (thin wires) offer more resistance than thick (thin wires) offer more resistance than thick wireswires

3.3. Material:Material: the type of material affects the the type of material affects the resistance (Al has higher resistance than Cu)resistance (Al has higher resistance than Cu)

4.4. Temperature:Temperature: the higher the temperature the the higher the temperature the higher the resistancehigher the resistance

Why are resistors needed?Why are resistors needed?

……to control current across a conductor.to control current across a conductor.

Consider your household voltage:* The voltage is constant at the outlet* Some appliances cannot handle the amount of current that is available in the wire (based on voltage and wire size)* Resistors are used in the appliances to

limit the current that they see

SuperconductorsSuperconductorsMaterials that have no resistance below Materials that have no resistance below a critical temperaturea critical temperature

Once a current is established in them, Once a current is established in them, the current continues even if the the current continues even if the potential difference source is removed!!potential difference source is removed!!

QuestionsQuestions

1.How much current would a 10.2 ohm toaster draw when attached to a 120 V outlet?

Ans: 12 A

2. An ammeter registers 2.5 A of current in a wire that is connected to a 9.0 V battery. What is the wire’s resistance?

Ans: 3.6 ohms

About batteries……About batteries……

Cathode:Gives electrons,(thus becomes positive)

Anode:Gets electrons(thus becomes negative)

What’s happening in a simple circuit?What’s happening in a simple circuit?1. Chemical energy stored in the battery is converted to the electrical energy of the charge carriers

2. The charge move from one battery terminal through the wire, which has very little resistance (because it’s a good conductor)

3. The charge gets to the light bulb, which has higher resistance. In the light bulb the charge loses electrical potential energy due to collisions. The PEelec is converted to internal energy, and the light bulb filament heats up, causing the glow.

4. The charge returns to the other battery terminal with zero potential energy. As the charge moves back across the battery to the other terminal, the battery does work on the charge and the charge gains PEelec.

19.3 Electric Power19.3 Electric Power

ObjectivesObjectives

1.1. Relate electric power to the rate at Relate electric power to the rate at which electrical energy is converted which electrical energy is converted to other forms of energyto other forms of energy

2.2. Calculate electric powerCalculate electric power

3.3. Calculate the cost of running Calculate the cost of running electrical applianceselectrical appliances

Electrical PowerElectrical Power

……..the rate at which the charge ..the rate at which the charge carriers do work.carriers do work.

Aka: the rate at which the charge Aka: the rate at which the charge carriers convert electrical carriers convert electrical potential energy to non-electrical potential energy to non-electrical forms of energy.forms of energy.

Equations for PowerEquations for Power

Power is the Power is the raterate at which work is doneat which work is done

P = W = ΔPE Δt Δt

Since ΔPE = qΔV, then P = qΔV Δt

But from 19.1 we know I = q Δt

So that leaves us with…..

P = IΔV

P = I2R

units of P (power) is watts (W)

Electric Power Usage

ENERGY usage and electrical billing is based on kilowatt-hours

Power companies charge for ENERGY usage, not POWER (watts) usage

Instead of charging for each watt (or kilowatt) you use, they charge for each kilowatt you use for each hour you use it

Kilowatt-hour vs Joules

kW-hr and J are both units of energy

1 kW-hr x 103 W x 60 min x 60 sec = 3.6 x 106 W-sec 1 kW 1 hr 1 min

And 1 W-sec = 1 J

So, 1 kW-hr = 3.6 x 106 J

Why High Voltage in Power Lines?Why High Voltage in Power Lines?

Recall that P=I2R, and this is the rate at which charge carriers lose potential energy (they lose potential energy because the potential energy is being converted to another form of energy)

So, the energy loss across any resistor is proportional to the resistance and the square of the current. To reduce this energy loss, you can either reduce resistance (R), or reduce current (I).

Since P=IΔV, as you reduce current (I) you must also increasevoltage (ΔV) in order to transmit the same amount of power.

Power to Your HomePower to Your Home

High voltage lines fromthe power plant transmit at voltages as high as 765,000 V

Transformers are usedto step down the voltageto ~ 4,000 V within the city

Transformers are usedagain to step down the voltage to your home to 120 V

QuestionsQuestions1. The operating potential difference of a light bulb is 120 V. The power rating of the bulb is 75 W.

a) What is the current in the bulb?b) What is the bulb’s resistance?

2. A steam iron draws 6.0 A when plugged into a 120 V outlet.

a) What is the power rating of this iron?b) How many joules of energy are

produced in 20.0 min?c) How much does it cost to run the

iron for 20.0 min at $0.010 per kW-hr

AnswersAnswers

1. a) 0.62 Ab) 190 Ω

2. a) 720 Wb) 8.6x105 Jc) $0.0024

Circuit Fluid ModelCircuit Fluid Model

In the water analogy, water flowed becausethere was a difference in gravitational potential energy between the full tank and the empty tank.

In a circuit, the battery provides the potentialdifference that “pushes” the charges to flow. The wires are the pipes the charges flow through. A lamp or resistor would be like a water wheel in a water circuit.