PHYSICS MR. BALDWINOhm’s Law 31 March 2014

AIM: Upon what factors does resistance depend?DO NOW: QUIZTake out a sheet of paper and answer the questions that follow

BALDWIN 2

1. What is the name given to a charged atom or molecule (one that gains or loses electrons)?

2. When an atom loses an electron, what happens to its net charge?

3. What is the name given to such atom that loses electrons?

4. When an atom gains an electron, what happens to its net charge?

5. What is the name given to such atom that gains electrons?

CHARGED PARTICLESCHARGED PARTICLES

1. ION: When an atom or molecule gains or loses an electron, it becomes charged.

2. ANION: negatively charged ion When an atom gains electrons, its net

charge is negative

3. CATION: positively charged ion When an atom loses electrons, its net

charge is positive

The Electric BatteryThe Electric BatteryVolta discovered that electricity could be created if dissimilar metals (electrodes) were connected by a conductive solution called an electrolyte.

This is a simple electric cellsimple electric cell.

A battery transforms chemical energy into electrical energy.

The Electric BatteryThe Electric BatteryElectrode that attracts anions is called an ANODE (+)

Electrode that attracts cations is called a CATHODE (–)

PHYSICS MR. BALDWINOhm’s Law April 1, 2014AIM: Upon what factors does the resistance of a conductor depend?DO NOW: QUIZTake out a sheet of paper and answer the questions that follow

Recall: Electric CurrentRecall: Electric CurrentElectric current (I) is the rate of flow of positive charges through a conductor:

where qq is the charge and tt is the time

Unit of electric current: the ampere, A.

1 A = 1 C/s.

qI

t

Recall: ChargesRecall: ChargesThe charge (q) is the number of positive charges :

neq

Ce 19106.1

What is the magnitude of the charge of an electron?

What is the typical UNIT of a charged object?

CCmbmicroCoulo 610

TEST YOURSELFTEST YOURSELF• Calculate the current

where 10 coulombs of charge pass a point in 5 seconds.

• Calculate the current in a lightning bolt that delivers a charge of 35 coulombs to the ground in 1ms.

10 ; 5

102.0

5

q C t s

q CI A

t s

3

3

35 ;

1 10

3535

10

q C

t ms s

q CI kA

t s

BALDWIN 11

A current of 5.0 A passes through the bulb in 20 µs. If the charge of an electron is 1.6 x 10-19 C, how many electrons flow through the bulb?

1419

4

45

5

1025.6106.1

100.1?

100.1100.220

100.20.5?0.5

C

Cn

e

qnn

Cqsst

sAqtIqqAI

SolveSubstituteUnknownGiven

TEST YOURSELFTEST YOURSELF

Resistance & Resistivity

The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area:

The constant ρ is called the resistivity and is a characteristic of the material. It’s unit is the m

The conducting ability of a material is often indicated by its resistivity. The lower the resistivity, the better the conductivity.

Variation of resistance with length and area: the analogy to water flow

How do you think the flow rate will be affected if you increase the cross-sectional area or length of the pipe along which the water has to flow?

resistance increases with lengthresistance decreases with diameter or cross-sectional area

Resistivity

Observation

• Looking at the table of Resistivity, which metal material is the most conductive?

• Which metal is the least conductive?

• Which substance is the least conductive and why?

PracticePractice

• L = 1609 m,

• A = πR2

• ρ= 1.7 x 10-8 Ωm.

First, find the cross-sectional area:

A = π•r2 = (3.14) • [ (0.002117 m) / 2)]2 = 3.519 x 10-6 m2

Now, substitute into the above equation to determine the resistance.

R = (1.7 x 10-8 Ωm) • (1609 m) / (3.519 x 10-6 m2)

R = 7.8 (7.7709 ohm)

Determine the resistance of a 1-mile length of 12-gauge copper wire. (Hint:1 mile = 1609 m; diameter of 12 gauge copper wire = 0.2117 cm)

PHYSICS MR. BALDWINOhm’s Law April 2, 2014AIM: How does the temperature, area and length of a conductor affects the resistance?

DO NOW: QUIZDetermine the resistance of a 1-m length of 12-gauge gold wire. (Hint: diameter of 12 gauge wire = 0.2117 cm)

Mathematical Reasoning

• Two wires - A and B - with circular cross-sections have identical lengths and are made of the same material. Yet, wire A has four times the resistance of wire B. How many times greater is the diameter of wire B than wire A?

Resistivity & Temperature

For any given material, the resistivity increases with temperature:

where T is temperature in 0C and is the thermal coefficient with unit 0C-1 or /0C.

Resistivity

RECALL: Resistance & Resistivity

The constant ρ is called the resistivity and is a characteristic of the material. It’s unit is the m

June 2011A circuit contains a 12.0-volt battery, an ammeter, a variable resistor, and connecting wires of negligible resistance, as shown below. A variable resistor made of nichrome wire is maintained at 20.°C. The length of the nichrome wire may be varied from 10.0 centimeters to 90.0 centimeters. The ammeter reads 2.00 amperes when the length of the wire is 10.0 centimeters.

Determine the resistance of the 10.0-centimeter length of nichrome wire. [1]

Calculate the cross-sectional area of the nichrome wire. [Show all work, including the equation and substitution with units.] [2]

June 2010

A 3.50-meter length of wire with a cross-sectional

area of 3.14 × 10–6 m2 is at 20° Celsius. The current in the wire is 24.0 amperes when connected to a 1.50-volt

source of potential difference.

Determine the resistance of the wire. [1]

Calculate the resistivity of the wire. [Show all

work, including the equation and substitution

with units.] [2]

PHYSICS MR. BALDWINOhm’s Law 3 April, 2014AIM: What is the relationship between the current and resistance in a circuit? (What is Ohm’s Law?) DO NOW: QUIZ1.What is electrical resistance?2.What variables(factors) do you think might affect electrical resistance in an electric conductor?

HOMEWORK: Worksheet 13.3 Ohm’s Law

• opposition to the flow/passage of an electric current through a conductor.

• factors affecting resistance:– Length of conductor– Cross-sectional area– Substance– Temperature

Simple CircuitSimple Circuit

In order for current to flow, there MUST be a path from one battery terminal, through the circuit, to the other battery terminal AND a potential difference across the terminal.

Which one of these circuits will work?

(c)

THIS ONE

Simple Circuit SchematicSimple Circuit SchematicA complete circuit is one where current can flow all the way around. By convention, current is defined as the flow of positive charges from + to – (high potential to low potential). Electrons actually flow in the opposite direction.

Simple Circuit must contain?Simple Circuit must contain?

Battery (power source)Battery (power source)

Conductor (wire)Conductor (wire)

Device Device

SwitchSwitch

Ohm’s LawOhm’s Law

Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends:

Ohm’s Law: GraphicallyOhm’s Law: Graphically

Materials that do not follow Ohm’s law are called nonohmicnonohmic.

Ohm’s Law: MathematicallyOhm’s Law: Mathematically

The ratio of the voltage to the current in a circuit is called the resistanceresistance..

Unit of resistanceUnit of resistance: the ohm, Ω.

1 Ω = 1 V/A.

1.5 V 3 0.50 Amp

BatteryVoltage(V)

TotalResistance(Ω)

Current(Amps)

3.0 V 3 1 Amp

4.5 V 3 1.5 Amp

Electric HazardsElectric Hazards

Even very small currents: 10 to 100 mA 10 to 100 mA can be dangerous, disrupting the nervous system.

Larger currents may also cause burns.

Household voltage can be lethal if you are wet and in good contact with the ground. SO…Be careful boys & girls!

Some clarifications:

• Batteries maintain a (nearly) constant potential difference; the current varies.

• Resistance is a property of a material or device.

• Current is not a vector but it does have a direction.

• Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.

Summarize the following termsSummarize the following terms

• Ion

• Anion

• Cation

• Anode

• Cathode

• Current

• Circuit

Resistors

Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision.

Resistors

http://www.physicslessons.com/exp22b.htm

Electric Power

Power, as in kinematics, is the energy transformed by a device per unit time.

In electricity, recall

energy transformed QV QP= = V=IV

time t t

Electric Power

The unit of power is the Watt, W.

For Ohmic devices, we can make the substitutions:

Electric Power

What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time.

We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kWh.

Alternating Current

Current from a battery flows steadily in one direction (direct current, DC).

Current from a power plant varies sinusoidally (alternating current, AC).

Superconductivity

In general, resistivity decreases as temperature decreases. Some materials, however, have resistivity that falls abruptly to zero at a very low temperature, called the critical temperature, TC.

BALDWIN 44

PHYSICS Prof.BALDWINELECTRICITY 10 April 2014

AIM: How do we determine the equivalent resistance in series circuits?

DO NOW:

Draw a simple series circuit and describe its characteristics in terms of the current and voltages (potential differences).

DC Circuits

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab

Resistors in Series

A series connection has a single path from the battery, through each circuit element in turn, then back to the battery.

An ammeter measures the current through a circuit component.

The same current going through the component must go through the ammeter, so there can be only one current path.

A connection with only one current path is called a series connection.

Diagramming Circuits

Resistors in Series

The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage.

Resistors in Series

From this we get the equivalent resistance (that single resistance that gives the same current in the circuit).

Resistors in Series

Determine the equivalent resistance

BALDWIN 51

PRACTICE: Determine

a. the equivalent resistance in the circuitb. The total current in the circuit c. The current in each componentd. the voltage drop across each resistor

REGENTS QUESTION

A 3.0-ohm resistor and a 6.0-ohm resistor are connected in series in an operating electric circuit. If the current through the 3.0-ohm resistor is 4.0 amperes, what is the potentialdifference across the 6.0-ohm resistor?(1) 8.0 V (3) 12 V(2) 2.0 V (4) 24 V

BALDWIN 53

PHYSICS Prof.BALDWINELECTRICITY 10 April 2014

AIM: How do we determine the equivalent resistance in parallel circuits?

DO NOW: QUIZ( you will have 10 minutes to complete

the following problem.)

Consider the following diagram. Calculate:a. the equivalent resistance of the resistor combinationb. the current in the circuitc. the potential drop across each resistord. the power dissipated across each resistor (extra credit)

Any time the current has two or more paths to follow, the circuit is considered a parallel circuit.

https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab

Diagramming Circuits

Resistors in Parallel

A parallel connection splits the current, the current in each component is different; the voltage across each resistor is the same:

Question?

• What do you think will happen when one of the bulbs go out?

• More current flows in the other paths making the other bulbs brighter

Resistors in Parallel

The total current is the sum of the currents across each resistor:

Resistors in Parallel

This gives the reciprocal of the equivalent resistance:

NOTE!!! Req< any of the resistors

BALDWIN 60

Solving problems involving complex circuits:

Calculate the equivalent resistance of the circuit?

Consider the following diagram. Calculate:a. the equivalent resistance of the resistor combinationb. the current in the circuitc. the current across each resistord. the power dissipated across each resistor

Draw the table in your notebook, perform the Draw the table in your notebook, perform the calculations and calculations and FillFill in the spaces in the spaces

R1 R2 R3 TOTAL

Resistance OhmsCurrent AmpsVoltage Volts

Power Watts

R1 R2 R3 TOTAL

Resistance 10 k 2 k 1 k 625 OhmsCurrent 0.9 m 4.5 m 9.0 m 14.4 m AmpsVoltage 9 9 9 9 Volts

Power 8.1 m 40.5 m 81 m 129.6 m Watts

Ammeters, Voltmeters & Ohmmeters

• An ammeter measures current and must be connected in series to measure the current;

• A voltmeter measures voltage and must be connected in parallel to measure the voltage.

• An ohmmeter measures resistance and requires a battery to provide a current. It too must be connected in parallel to measure the resistance.