Electrical Energy StorageElectrical Energy Storage

◊ ◊ We can store electric energy in a We can store electric energy in a capacitor capacitor ::

◊ ◊ Found in nearly all electronic circuits eg. in photo-flash units.Found in nearly all electronic circuits eg. in photo-flash units.

◊ ◊ Simplest is: two close but separated parallel plates. Simplest is: two close but separated parallel plates. When connected to a battery electrons get transferred fromWhen connected to a battery electrons get transferred from one plate to the other until the potential difference betweenone plate to the other until the potential difference between them = voltage of battery.them = voltage of battery.

◊ ◊ How?How?

Positive battery terminal attracts electrons on LH plate; these Positive battery terminal attracts electrons on LH plate; these are then pumped through battery, through the terminal to the are then pumped through battery, through the terminal to the opposite plate. Process continues until no more potential opposite plate. Process continues until no more potential difference btn plate and connected terminal.difference btn plate and connected terminal.

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◊ ◊ Discharging: when conducting path links the two charged plates.

◊◊ Discharging is what creates the flash in a camera.

♦If very high voltages (eg caps in tv’s), its dangerous if you are this path!

animation ????

Potential difference or Voltage (symbol V)

• When the ends of an electric conductor are at different electric potential, charge flows from one end to the other. Voltage is what causes charge to move in a conductor. Charge moves toward lower potential energy the same way as you would fall from a tree.

• Voltage plays a role similar to pressure in a pipe; to get water to flow there must be a pressure difference between the ends, this pressure difference is produced by a pump

• A battery is like a pump for charge, it provides the energy for pushing the charges around a circuit

Voltage and current are not the same thingVoltage and current are not the same thing

• You can have voltage, but without a You can have voltage, but without a path (connection) there is no current.path (connection) there is no current.

voltagevoltage

An An electricalelectrical

outletoutlet

Current– flow of electric chargeCurrent– flow of electric charge

If I connect a battery to the ends of the copper bar the If I connect a battery to the ends of the copper bar the electrons in the copperelectrons in the copper will be pulled toward the positive will be pulled toward the positive side of the battery and will flow around and around.side of the battery and will flow around and around. this is called this is called currentcurrent – flow of charge – flow of charge

coppercopper

DuracellDuracell

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An electric circuit!An electric circuit!

Electric current (symbol I)Electric current (symbol I)

• DEF: the rate at which charge flows DEF: the rate at which charge flows past a given cross-section.past a given cross-section.

• measured in amperes (A)

q

◊ the flow of electric charge q that can occur in solids, liquids and gases.

qI =

t1C

1A = 1s

Solids – electrons in metals and graphite, and holes in semiconductorsLiquids – positive and negative ions in molten and aqueous electrolytesGases – electrons and positive ions stripped from gaseous molecules by large potential differences.

Electrical resistance (symbol R)Electrical resistance (symbol R)

• Why is it necessary to keep pushing the charges to make Why is it necessary to keep pushing the charges to make them move?them move?

• The electrons do not move unimpeded through a The electrons do not move unimpeded through a conductor. As they move they keep bumping into the ions conductor. As they move they keep bumping into the ions of crystal lattice which either slows them down or bring of crystal lattice which either slows them down or bring them to rest.them to rest.

..

atoms

free electronfree electron

(actually positive ions)

path

The The resistance (R)resistance (R) is a measure of the degree to is a measure of the degree to which the conductor impedes the flow of current.which the conductor impedes the flow of current.Resistance is measured in Resistance is measured in OhmsOhms ( ())

OHM’S LAW - Current, Voltage and ResistanceOHM’S LAW - Current, Voltage and Resistance

• DEF: Current through resistor (conductor) is proportional to potential difference on the resistor if the temperature of a resistor is constant

(the resistance of a conductor is constant).

VI =

R

voltagecurrent =

resistance◊ ◊ math def: math def:

• if resistance R is constant/ temperature is constant if resistance R is constant/ temperature is constant • I – current V – potential difference across RI – current V – potential difference across R

ExamplesExamples

• If a 3 volt flashlight bulb has a resistance of 9 ohms, how If a 3 volt flashlight bulb has a resistance of 9 ohms, how much current will it draw?much current will it draw?

• I = V / R = 3 V / 9 I = V / R = 3 V / 9 = 1/3 Amps = 1/3 Amps

• If a light bulb draws 2 A of current when connected to a If a light bulb draws 2 A of current when connected to a 120 volt circuit, what is the resistance of the light bulb?120 volt circuit, what is the resistance of the light bulb?

• R = V / I = 120 V / 2 A = 60 R = V / I = 120 V / 2 A = 60

Effects of electric current on the BODY- electric shockEffects of electric current on the BODY- electric shock

Current (A)Current (A) EffectEffect

0.0010.001 can be feltcan be felt

0.0050.005 painfulpainful

0.0100.010 involuntary muscle contractions (spasms)involuntary muscle contractions (spasms)

0.0150.015 loss of muscle controlloss of muscle control

0.0700.070if through the heart, serious disruption; probably if through the heart, serious disruption; probably fatal if current lasts for more than 1 secondfatal if current lasts for more than 1 second

questionable circuits: live (hot) wire ? how to avoid being electrified?questionable circuits: live (hot) wire ? how to avoid being electrified?

1.1. keep one hand behind the body (no hand to hand current through the body)keep one hand behind the body (no hand to hand current through the body)

2. touch the wire with the back of the hand. Shock causing muscular contraction 2. touch the wire with the back of the hand. Shock causing muscular contraction will not cause their hands to grip the wire. will not cause their hands to grip the wire.

human body resistance varies: human body resistance varies: 100 ohms if soaked with salt water; 100 ohms if soaked with salt water; moist skin - 1000 ohms; moist skin - 1000 ohms; normal dry skin – 100 000 ohms, normal dry skin – 100 000 ohms, extra dry skin – 500 000 ohmsextra dry skin – 500 000 ohms..

What would be the current in your body if you touch the What would be the current in your body if you touch the terminals of a 12-V battery with dry hands?terminals of a 12-V battery with dry hands?

I = V/R = 12 V/100 000 I = V/R = 12 V/100 000 = 0.000 12 A quite harmless = 0.000 12 A quite harmless

But if your hands are moist (fear of AP test?) and you But if your hands are moist (fear of AP test?) and you touch 24 V battery, how much current would you draw?touch 24 V battery, how much current would you draw?

I = V/R = 24 V/1000 I = V/R = 24 V/1000 = 0.024 A = 0.024 A a dangerous amount of current.a dangerous amount of current.

Factors affecting resistanceFactors affecting resistance

The units of resistance are volts per ampere (VAThe units of resistance are volts per ampere (VA-1-1).).However, a separate SI unit called the ohm Ω is defined However, a separate SI unit called the ohm Ω is defined as the resistance through which a current of 1 A flows as the resistance through which a current of 1 A flows when a potential difference of 1 V is applied.when a potential difference of 1 V is applied.

VR =

I

Conductors, semiconductors and insulators differ Conductors, semiconductors and insulators differ in their resistance to current flow.in their resistance to current flow.

DEF: The electrical resistance of a piece of material DEF: The electrical resistance of a piece of material is defined by the ratio of the potential difference is defined by the ratio of the potential difference across the material to the current that flows through it.across the material to the current that flows through it.

Wires, wires, wires Wires, wires, wires

As you are going to see, the resistance of a wire can be As you are going to see, the resistance of a wire can be completely ignored – if it is a thin wire connecting two, completely ignored – if it is a thin wire connecting two, three or more resistors, or becoming very important if it is three or more resistors, or becoming very important if it is a long, long wire as in the case of iron, washing a long, long wire as in the case of iron, washing machine, toaster ….., where it becomes resistor itself. machine, toaster ….., where it becomes resistor itself.

The resistance of a conducting wire depends on four main The resistance of a conducting wire depends on four main factors:factors: • length • cross-sectional area • resistivity • temperature• length • cross-sectional area • resistivity • temperature

Cross Sectional Area (A)Cross Sectional Area (A)

The cross-sectional area of a conductor (thickness) is similar to the cross section The cross-sectional area of a conductor (thickness) is similar to the cross section of a hallway. If the hall is very wide, it will allow a high current through it, while a of a hallway. If the hall is very wide, it will allow a high current through it, while a narrow hall would be difficult to get through. Notice that the electrons seem to be narrow hall would be difficult to get through. Notice that the electrons seem to be moving at the same speed in each one but there are many more electrons in the moving at the same speed in each one but there are many more electrons in the larger wire. This results in a larger current which leads us to say that the larger wire. This results in a larger current which leads us to say that the resistance is less in a wire with a larger cross sectional area.resistance is less in a wire with a larger cross sectional area.

Length of the Conductor (L)Length of the Conductor (L)

The length of a conductor is similar to the length of a hallway. The length of a conductor is similar to the length of a hallway. A shorter hallway will result in less collisions than a longer one. A shorter hallway will result in less collisions than a longer one.

TemperatureTemperature

To understand the effect of temperature you must picture what happens in a To understand the effect of temperature you must picture what happens in a conductor as it is heated. Heat on the atomic or molecular scale is a direct conductor as it is heated. Heat on the atomic or molecular scale is a direct representation of the vibration of the atoms or molecules. Higher temperature representation of the vibration of the atoms or molecules. Higher temperature means more vibrations. In a cold wire ions in crystal lattice are not vibrating much so means more vibrations. In a cold wire ions in crystal lattice are not vibrating much so the electrons can run between them fairly rapidly. As the conductor heats up, the the electrons can run between them fairly rapidly. As the conductor heats up, the ions start vibrating. As their motion becomes more erratic they are more likely to get ions start vibrating. As their motion becomes more erratic they are more likely to get in the way and disrupt the flow of the electrons. As a result, the higher the in the way and disrupt the flow of the electrons. As a result, the higher the temperature, the higher the resistance. temperature, the higher the resistance. At extremely low temperatures, some materials, known as superconductors, have At extremely low temperatures, some materials, known as superconductors, have no measurable resistance. This is called superconductivity. Gradually, we are no measurable resistance. This is called superconductivity. Gradually, we are creating materials that become superconductors at higher temperatures and the creating materials that become superconductors at higher temperatures and the race is on to find or create materials that superconduct at room temperature. We race is on to find or create materials that superconduct at room temperature. We are painfully far away from the finish line. are painfully far away from the finish line.

Resistance also depends on temperature, usually increasing as the temperature increases.

At low temperatures some materials, known as superconductors, have no resistance at all. Resistance in wires produces a loss of energy (usually in the form of heat), so materials with no resistance produce no energy loss when currents pass through them.

And that means, once set up in motion (current) you don’t need to add additional energy in oder to keep them going.

The dream: current without cost!!!!!!!!! Both in money and damage to environment!!!!!!!!

Resistance of a wire when the temperature is kept Resistance of a wire when the temperature is kept constantconstant is: is:

LR = ρ

AThe resistivity, The resistivity, ρρ (the Greek letter rho), is a value that only (the Greek letter rho), is a value that only depends on the material being used. It is tabulated and you depends on the material being used. It is tabulated and you can find it in the books. For example, gold would have a lower can find it in the books. For example, gold would have a lower value than lead or zinc, because it is a better conductor than value than lead or zinc, because it is a better conductor than they are.they are.The unit is The unit is Ω•m. Ω•m.

Of course, resistance depends on the material being used.Of course, resistance depends on the material being used.

In conclusion, we could say that a short fat cold wire makes In conclusion, we could say that a short fat cold wire makes the best conductor.the best conductor.

If you double the length of a wire, you will double the If you double the length of a wire, you will double the resistance of the wire. resistance of the wire.

If you double the cross sectional area of a wire you will cut If you double the cross sectional area of a wire you will cut its resistance in half.its resistance in half.

ExampleExample

A copper wire has a length of 160 m and a diameter of 1.00 mm. If the wire is A copper wire has a length of 160 m and a diameter of 1.00 mm. If the wire is connected to a 1.5-volt battery, how much current flows through the wire? connected to a 1.5-volt battery, how much current flows through the wire?

The current can be found from Ohm's Law, V = IR. The V is the battery The current can be found from Ohm's Law, V = IR. The V is the battery voltage, so if R can be determined then the current can be calculated. voltage, so if R can be determined then the current can be calculated. The first step, then, is to find the resistance of the wire: The first step, then, is to find the resistance of the wire:

L = 1.60 m.L = 1.60 m.r = 1.00 mmr = 1.00 mm = 1.72x10= 1.72x10-8-8 m, copper - booksm, copper - books

The current can now be found from Ohm's Law: The current can now be found from Ohm's Law:

The resistance of the wire is then:The resistance of the wire is then:

R = R = L/A = (1.72x10L/A = (1.72x10-8-8 m)(1.67)/(7.85x10m)(1.67)/(7.85x10-7-7mm22 ) = 3.50 ) = 3.50

I = V / R = 1.5 / 3.5 = 0.428 A I = V / R = 1.5 / 3.5 = 0.428 A

Ohmic and Non-Ohmic conductorsOhmic and Non-Ohmic conductors

How does the current varies with potential difference for some typical devices?How does the current varies with potential difference for some typical devices?cu

rren

tcu

rren

t

potential potential differencedifference

devices are non-ohmic ifdevices are non-ohmic ifresistance changesresistance changes

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metal at const. temp. filament lamp diode metal at const. temp. filament lamp diode

I 1 = is const. R is const.V R

Devices for which current through them is directly Devices for which current through them is directly proportional to the potential difference across device proportional to the potential difference across device are said to be ‘ohmic devices’ or ‘ohmic conductors’ or are said to be ‘ohmic devices’ or ‘ohmic conductors’ or simply simply resistorsresistors. There are very few devices that are . There are very few devices that are trully ohmic. However, many useful devices obey the trully ohmic. However, many useful devices obey the law at least over a reasonable range.law at least over a reasonable range.

When a current is flowing through a load such as a resistor, it When a current is flowing through a load such as a resistor, it dissipates energy in itdissipates energy in it. In collision with lattice ions electrons’ . In collision with lattice ions electrons’ kinetic energy is transferred to the ions, and as a result the kinetic energy is transferred to the ions, and as a result the amplitude of vibrations of the ions increases and therefore the amplitude of vibrations of the ions increases and therefore the temperature of the device increases.temperature of the device increases.That thermal energy (internal energy) is then transferred as heat That thermal energy (internal energy) is then transferred as heat (to the air, food, hair etc.) by convection, or radiated as light (to the air, food, hair etc.) by convection, or radiated as light (electric bulb). (electric bulb).

Where is that energy coming from? Where is that energy coming from? This energy is equal to the potential energy lost by the charge as This energy is equal to the potential energy lost by the charge as it moves through the potential difference that exists between the it moves through the potential difference that exists between the terminals of the load.terminals of the load.

DEF: Power is the rate at which electric energy is converted DEF: Power is the rate at which electric energy is converted into another form such as mechanical energy, heat, or light.into another form such as mechanical energy, heat, or light.

Power dissipation in resistorsPower dissipation in resistors

DEF: Electric power is the rate at which energy DEF: Electric power is the rate at which energy is supplied to or used by a device.is supplied to or used by a device.

Power is measured in J sPower is measured in J s-1-1 called watts W. called watts W.

If a vacuum cleaner has a power rating of 500 W, it meansIf a vacuum cleaner has a power rating of 500 W, it meansit is converting electrical energy to mechanical, soundit is converting electrical energy to mechanical, soundand heat energy at the rate of 500 J sand heat energy at the rate of 500 J s-1-1. A 60 W light globe. A 60 W light globeconverts electrical energy to light and heat energy at theconverts electrical energy to light and heat energy at therate of 60 J s rate of 60 J s -1-1..

Appliance Power rating

Blow heater 2 kWKettle 1.5 kWToaster 1.2 kWIron 850 WVacuum cleaner 1.2 kWTelevision 250 W

Basic definition of power:Basic definition of power:

Deriving expressions for determining powerDeriving expressions for determining power

WP =

t

Remember: W = qV Remember: W = qV → and I = q/t, so→ and I = q/t, soqV

P = t

P = I VP = I V 1J

1W = = 1A 1V1s

P = IV = VP = IV = V22/R = I/R = I22 R R

Look at your hair dryer. If label says “10 A”, that means that the power of Look at your hair dryer. If label says “10 A”, that means that the power of the hair dryer is 10x120=1200 W, or 1.2 kW (using a standard US 120 V the hair dryer is 10x120=1200 W, or 1.2 kW (using a standard US 120 V outlet). outlet).

In USA you can not get direct information on power of applianceIn USA you can not get direct information on power of appliance you buy. you buy.

Comparison of US and other countries that use voltage of 240 V. Comparison of US and other countries that use voltage of 240 V.

As the power of appliances is the roughly the same, the As the power of appliances is the roughly the same, the appliances in USA have to draw a greater current, hence have to appliances in USA have to draw a greater current, hence have to have less resistance. As the consequence the wires (both used have less resistance. As the consequence the wires (both used for connecting and in appliances) are thicker in USA.for connecting and in appliances) are thicker in USA.

exampleexample

• How much current is drawn by a 60 Watt light bulb connected to a How much current is drawn by a 60 Watt light bulb connected to a 120 V power line?120 V power line?

P = 60 W = I V = I x 120 P = 60 W = I V = I x 120

so I =so I = 0.5 A0.5 A• What is the resistance of the bulb?What is the resistance of the bulb?

I = V/R R = V/I = 120 V/0.5 A I = V/R R = V/I = 120 V/0.5 A

R = 240 R = 240

Paying for electricityPaying for electricity

• You pay for the total amount of electrical energy (not power) that You pay for the total amount of electrical energy (not power) that is used each monthis used each month

• In Irving the cost of electric energy used is 14 In Irving the cost of electric energy used is 14 ¢ ¢ per kilowatt-hour. per kilowatt-hour. • How do we get kilowatt-hour and what is that? How do we get kilowatt-hour and what is that? • Power = energy/timePower = energy/time• Energy = power x time, so energy can be expressed in units Energy = power x time, so energy can be expressed in units

watts x second what is simply a joule.watts x second what is simply a joule.

Physicists measure energy in joules, but utility companies Physicists measure energy in joules, but utility companies customarily charge energy in units of kilowatt-hours (kW h), where :customarily charge energy in units of kilowatt-hours (kW h), where :

Kilowatt-hour (kWh) = 10Kilowatt-hour (kWh) = 1033 W x 3600 s W x 3600 s

1 kWh = 3.6 x 101 kWh = 3.6 x 1066 J J

1W x 1s = 1J1W x 1s = 1J

$$$ example $$$$$$ example $$$

• At a rate of 14 cents per kWh, how much does it cost to keep a 100 W At a rate of 14 cents per kWh, how much does it cost to keep a 100 W light bulb on for one day?light bulb on for one day?

• energy (kWh) = power (kW) x time (h) energy (kWh) = power (kW) x time (h)

• energy (kWh) = 0.1 kW x 24 h = 2.4 kWhenergy (kWh) = 0.1 kW x 24 h = 2.4 kWh

cost / day = 2.4 kWh x 14 cents/kWh = 33.6 cost / day = 2.4 kWh x 14 cents/kWh = 33.6 ¢¢

for one month that amounts to for one month that amounts to $ 10.1.$ 10.1.

Direct Current (DC) electric circuitsDirect Current (DC) electric circuits• a circuit containing a battery is a DC circuita circuit containing a battery is a DC circuit• in a DC circuit the current always flows in the in a DC circuit the current always flows in the same direction. same direction. • The direction of the current depends on how you connect the batteryThe direction of the current depends on how you connect the battery

Either way the bulb will be on.Either way the bulb will be on.

DuracellDuracell

+

The electrons go one way but the current flows the opposite to the opposite to the direction that the electrons travel.direction that the electrons travel.That’s convention.That’s convention.

• a circuit must provide a closed path for the a circuit must provide a closed path for the current to circulate aroundcurrent to circulate around

• when the electrons pass through the light when the electrons pass through the light bulb they loose some of their energy bulb they loose some of their energy the conductor (resistor) heats upthe conductor (resistor) heats up

• the battery is like a pump that re-the battery is like a pump that re-energizes them each time they pass energizes them each time they pass through itthrough it

hystoric explanationclick me

When a battery is connected across the ends of a metal When a battery is connected across the ends of a metal wire, an electric field is produced in the wire. wire, an electric field is produced in the wire. All free All free electrons in the circuit start moving at the same time.electrons in the circuit start moving at the same time. Free electrons are accelerated along their path ree electrons are accelerated along their path reaching enormous speeds of about 10reaching enormous speeds of about 1066 ms ms-1-1. They . They collide with positive ions of crystal lattice generating collide with positive ions of crystal lattice generating heat that causes the temperature of the metal to heat that causes the temperature of the metal to increse. increse. After this event, they are again accelerated After this event, they are again accelerated because of the electric field, until the next collision because of the electric field, until the next collision occurs.occurs. DDue to the collisions with positive ions of crystal ue to the collisions with positive ions of crystal lattice, hence changing direction, it is estimated that the lattice, hence changing direction, it is estimated that the drift velocity is only a small fraction of a metre each drift velocity is only a small fraction of a metre each second (about 10second (about 10-4-4 m s m s-1-1).).

Drift speedDrift speed

example: in an el. circuit of a car, electrons have example: in an el. circuit of a car, electrons have average drift speed of about 0.01 cm/s, so it takes average drift speed of about 0.01 cm/s, so it takes ~ 3 hour for an electron to travel through 1m. ~ 3 hour for an electron to travel through 1m.

it’s not even a snail’s pace!!!!!it’s not even a snail’s pace!!!!!

• the electricity that you get from the power company is not DC it is AC the electricity that you get from the power company is not DC it is AC (alternating) (alternating) created by an AC electric generatorcreated by an AC electric generator..

• In an In an AC circuit the current reverses direction periodicallyAC circuit the current reverses direction periodically

__ ++The current in AC electricity alternates in direction. The back-and-forth motion The current in AC electricity alternates in direction. The back-and-forth motion occurs at freq. of 50 or 60 Hz, depending on the electrical system of the country. occurs at freq. of 50 or 60 Hz, depending on the electrical system of the country.

AC movement of electrons in a wireAC movement of electrons in a wire

!!!!!!! the source of electrons is wire itself – free electrons in it !!!!!!!!!!!!! the source of electrons is wire itself – free electrons in it !!!!!! If you are jolted by electric shock, electrons making up the current in your body If you are jolted by electric shock, electrons making up the current in your body originate in your body. They do NOT come from the wire through your body into originate in your body. They do NOT come from the wire through your body into the ground. Alternating electric field causes electrons to vibrate. Small the ground. Alternating electric field causes electrons to vibrate. Small vibrations – tingle; large vibrations can be fatal.vibrations – tingle; large vibrations can be fatal.

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timetime

ACAC

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DCDC

How does the voltage and current change in time?How does the voltage and current change in time?

DC does not change DC does not change direction over time;direction over time;

the actual voltage in the actual voltage in a 120-V AC circuit a 120-V AC circuit varies between varies between +170V and -170V +170V and -170V peaks.peaks.

AC vs. DC currentAC vs. DC current

• for heaters, hair dryers, irons, toasters, waffle makers, for heaters, hair dryers, irons, toasters, waffle makers, the fact that the current reverses makes no difference. the fact that the current reverses makes no difference. They can be used with either AC or DC electricity.They can be used with either AC or DC electricity.

• battery chargers (e.g., for cell phones) convert the AC battery chargers (e.g., for cell phones) convert the AC to DCto DC

• Why do we use AC ?? DC seems simpler?Why do we use AC ?? DC seems simpler?• late 1800’s late 1800’s the war of the currents the war of the currents• Edison (DC) vs Tesla (Westinghouse) (AC)Edison (DC) vs Tesla (Westinghouse) (AC)• Edison opened the first commercial power plane for Edison opened the first commercial power plane for

producing DC in NY in 1892producing DC in NY in 1892• Tesla who was hired by George Westinghouse Tesla who was hired by George Westinghouse

believed that AC was superiorbelieved that AC was superior• Tesla was right, but Edison never gave up!Tesla was right, but Edison never gave up!

Why AC is better than DCWhy AC is better than DC

• DC power is provided at one voltage onlyDC power is provided at one voltage only

• The major advantage: AC voltages can be transformed The major advantage: AC voltages can be transformed to higher or lower voltages (can be stepped up or down to higher or lower voltages (can be stepped up or down to provide any voltage required)to provide any voltage required)

• This means that the high voltages used to send This means that the high voltages used to send electricity over great distances from the power station electricity over great distances from the power station can be reduced to a safer voltage for use in the house. can be reduced to a safer voltage for use in the house.

• This is done by the use of a transformer. This is done by the use of a transformer. • DC is very expensive to transmit over large distances DC is very expensive to transmit over large distances

compared to AC (more loss to heat), so many plants compared to AC (more loss to heat), so many plants are requiredare required

• DC power plants must be close to usersDC power plants must be close to users• AC plants can be far outside citiesAC plants can be far outside cities• by 1895 DC was out and AC was inby 1895 DC was out and AC was in

We have defined potential difference as the amount of We have defined potential difference as the amount of work that has to be done to move a unit positive charge work that has to be done to move a unit positive charge from one point to the other in an electric field. from one point to the other in an electric field.

Electromotive force (emf – Electromotive force (emf – εε oror E) E)

W ΔUΔV = =

q q

• DEF: DEF: emfemf (ε) of the source is the potential difference between (ε) of the source is the potential difference between the terminals when the terminals when NONO current flows to an external circuit. current flows to an external circuit.

(IT IS A VOLTAGE NOT A FORCE).(IT IS A VOLTAGE NOT A FORCE).

A battery or an electric generator that transforms one type of energy A battery or an electric generator that transforms one type of energy into electric energy is called into electric energy is called source ofsource of electromotive force electromotive force

In the true sense, electromotive force (emf) is the work (energy) per unit charge made available by an electrical source.

D.C. circuit analysisD.C. circuit analysis

An electric circuit has three essential componentsAn electric circuit has three essential components1. A source of emf.1. A source of emf.2. A conducting pathway obtained by conducting2. A conducting pathway obtained by conducting wires or some alternative.wires or some alternative.3. A load to consume energy such as a filament3. A load to consume energy such as a filament globe, other resistors and electronic components.globe, other resistors and electronic components.

Electric Circuits: Any path along which electrons can Electric Circuits: Any path along which electrons can flow is a circuit. For a continuous flow of electrons, flow is a circuit. For a continuous flow of electrons, there must be a complete circuit with no gaps. A gap is there must be a complete circuit with no gaps. A gap is usually provided by an electric switch that can be usually provided by an electric switch that can be opened or closed to either cut off or allow electron flow.opened or closed to either cut off or allow electron flow.

When the switch is closed, a current exists almost immediately in all circuit. The current does not “pile up” anywhere but flows through the whole circuit. Electrons in all circuit begin to move at once. Eventually the electrons move all the way around the circuit. A break anywhere in the path results in an open circuit, and the flow of electrons ceases.

Terminal voltage, emf and internal resistanceTerminal voltage, emf and internal resistance

In the circuit the total energy supplied is determined by the value of the emf. In the circuit the total energy supplied is determined by the value of the emf. When electrons flow around a circuit, they gain potential energy in the cell When electrons flow around a circuit, they gain potential energy in the cell and then lose the energy in the resistors. In a closed circuits charge must and then lose the energy in the resistors. In a closed circuits charge must flow between the electrodes of the battery and there is always some flow between the electrodes of the battery and there is always some hindrance to completely free flow. So when the current I is drawn from the hindrance to completely free flow. So when the current I is drawn from the battery there is some resistance called INTERNAL RESISTANCE (battery there is some resistance called INTERNAL RESISTANCE (rr ) of the ) of the battery causing the voltage between terminals to drop below the maximum battery causing the voltage between terminals to drop below the maximum value specified by the battery’s emf.value specified by the battery’s emf.

Thus the TERMINAL VOLTAGE (the actual voltage delivered) is:

V = - Ir

In the mid-nineteenth century, In the mid-nineteenth century, G.R. Kirchoff G.R. Kirchoff (1824-1887) stated two simple rules using the (1824-1887) stated two simple rules using the laws of conservation of energy and charge to laws of conservation of energy and charge to help in the analysis of direct current circuits.help in the analysis of direct current circuits.

These rules are called Kirchoff’s rules.These rules are called Kirchoff’s rules.

‘‘The sum of the currents flowing into a point in a circuit The sum of the currents flowing into a point in a circuit equals the sum of the currents flowing out at that point’.equals the sum of the currents flowing out at that point’.

1. Junction rule – conservation of charge. 1. Junction rule – conservation of charge.

II1 1 + I + I2 2 = I= I3 3 + I + I4 4 + I+ I55

2. loop rule – conservation of energy principle: Energy supplied 2. loop rule – conservation of energy principle: Energy supplied equals the energy released in this closed pathequals the energy released in this closed path

‘‘In a closed loop, the sum of the emfs equals In a closed loop, the sum of the emfs equals the sum of the potential drops’.the sum of the potential drops’.

V = VV = V11 + + VV22 + + VV3 3

• • Burning out of one of the lamp filaments or simply Burning out of one of the lamp filaments or simply opening the switch could cause such a break.opening the switch could cause such a break.

eq 1 2 3R = R + R + R

Resistors in SeriesResistors in Series

• • connected in such a way that all componentsconnected in such a way that all components have the same current through them.have the same current through them.

logic: the total or effective resistance would have length Llogic: the total or effective resistance would have length L11+ L+ L22+ L+ L33

and resistance is proportional to the lengthand resistance is proportional to the length

Equivalent or total or effective or resistance is the one that Equivalent or total or effective or resistance is the one that could replace all resistors resulting in the same current. could replace all resistors resulting in the same current.

Resistors in ParallelResistors in Parallel

• • Electric devices connected in parallel are Electric devices connected in parallel are connected to the same two points of an electric connected to the same two points of an electric circuit, so all components have the same circuit, so all components have the same potential difference across them.potential difference across them.• • The current flowing into the point of splitting is The current flowing into the point of splitting is equal to the sum of the currents flowing out at equal to the sum of the currents flowing out at that point: that point: I =I = II1 1 + I + I

2 2 + I+ I33..

• • A break in any one path does not interrupt the flow of charge in the A break in any one path does not interrupt the flow of charge in the other paths. Each device operates independently of the other devices. other paths. Each device operates independently of the other devices. The greater resistance, the smaller curent.The greater resistance, the smaller curent.

3

1 1 1

eq 1 2

1= + +

R R R R

equivelent resistance equivelent resistance is smaller than the is smaller than the smallest resistance.smallest resistance.

RESISTORS IN COMPOUND CIRCUITSRESISTORS IN COMPOUND CIRCUITS

Now you can calculate current, potential drop and Now you can calculate current, potential drop and power dissipated through each resistorpower dissipated through each resistor

example: Find power of the source, current in each resistor, terminal potential, example: Find power of the source, current in each resistor, terminal potential, potential drop across each resistor and power dissipated in each resistor.potential drop across each resistor and power dissipated in each resistor.

RReqeq = 120 = 120 I = I = εεRReqeq = 0.3 A = 0.3 A

terminal potential: V = terminal potential: V = εε – Ir = 36 – 0.3x6.7 = 34 V – Ir = 36 – 0.3x6.7 = 34 V

current through resistors 100current through resistors 100ΩΩ and 50 and 50ΩΩ : I = I : I = I11 + I + I22 I I11RR11 = I = I22RR22

0.3 = I0.3 = I11 + I + I22 100 I 100 I11 = 50 I = 50 I2 2 → → II11 = 0.1 A I = 0.1 A I22 = 0.2 A = 0.2 A

potential drops V = IR

power dissipated P = IV

80 Ω 0.3x80 = 24 V 0.3x24 = 7.2 W

100 Ω 0.1x100 = 10 V 0.1x10 = 1 W

50 Ω 0.2x50 = 10 V 0.2x10 = 2 W

6.7 Ω 0.3x6.7 = 2 V 0.3x2 = 0.6 W

εε = = ΣΣ all potential drops all potential drops

36 V = 2 V + 24 V + 10 V36 V = 2 V + 24 V + 10 V

power dissipated in the circuit = power dissipated in the circuit = power of the sourcepower of the source

0.6 + 2 + 1 + 7.2 = 0.3x36 0.6 + 2 + 1 + 7.2 = 0.3x36

In practical use, we need to be able to measure currents through In practical use, we need to be able to measure currents through components and voltages across various components in electrical components and voltages across various components in electrical circuits. To do this, we use circuits. To do this, we use AMMETERSAMMETERS and and VOLTMETERSVOLTMETERS..

Ammeters and voltmetersAmmeters and voltmeters

An ammeter – measures current passing through itAn ammeter – measures current passing through it

• • is is always connected in series always connected in series with a component we want to with a component we want to measure in order that whatever current passes through the measure in order that whatever current passes through the component also passes the ammeter.component also passes the ammeter.

• • has a very low resistance compared with thehas a very low resistance compared with theresistance of the circuit so that it will not alter theresistance of the circuit so that it will not alter thecurrent the current being measured.current the current being measured.

• • would ideally have no resistance with no potentialwould ideally have no resistance with no potentialdifference across it so no energy would bedifference across it so no energy would bedissipated in it.dissipated in it.

A voltmeter – measures voltage drop between two pointsA voltmeter – measures voltage drop between two points

• • is is always connected always connected across a device (across a device (in parallelin parallel).).

• • has a very high resistance so that it takes very littlehas a very high resistance so that it takes very littlecurrent from the device whose potential differencecurrent from the device whose potential differenceis being measured.is being measured.

• • an ideal voltmeter would have infinite resistancean ideal voltmeter would have infinite resistancewith no current passing through it and no energywith no current passing through it and no energywould be dissipated in it.would be dissipated in it.

A potential dividerA potential divider

In electronic systems, it is often necessary to obtain smallerIn electronic systems, it is often necessary to obtain smallervoltages from larger voltages for the various electronicvoltages from larger voltages for the various electroniccircuits. A circuits. A potential divider potential divider is a device that produces theis a device that produces therequired voltage for a component from a larger voltage.required voltage for a component from a larger voltage.It consists of a series of resistors or a rheostat (variableIt consists of a series of resistors or a rheostat (variableresistor) connected in series in a circuit. resistor) connected in series in a circuit.

Potential divider equationPotential divider equation

1 2

VI =

R +R 1 1V = IR

11

1 2

RV = V

R +R

In the potential divider shown, calculate:In the potential divider shown, calculate:(a) the total current in the circuit(a) the total current in the circuit(b) the potential difference across each resistor(b) the potential difference across each resistor(c) the voltmeter reading if it was connected(c) the voltmeter reading if it was connectedbetween terminals 2 and 6.between terminals 2 and 6.

example:example:

(a)(a) The total resistance R = 12 Ω. The total resistance R = 12 Ω.

I = V / R = 12 V / 12 Ω = 1 AI = V / R = 12 V / 12 Ω = 1 A

(b) 6 x V = 12 V (b) 6 x V = 12 V → V = 2 V (→ V = 2 V (12 V is equally shared by each 2 Ω resistor.12 V is equally shared by each 2 Ω resistor.

oror V = IR = 1x2 = 2 VV = IR = 1x2 = 2 V

(c) R = 4 x 2 = 8 (c) R = 4 x 2 = 8 Ω Ω (Between terminals 2 and 6 there are 4 resistors) (Between terminals 2 and 6 there are 4 resistors)

potential difference between the terminals ispotential difference between the terminals is

V = IR = 1 x 8 = 8 V V = IR = 1 x 8 = 8 V

Because resistance is directly proportional to the length of Because resistance is directly proportional to the length of a resistor, a variable resistor also known as a potentiometer a resistor, a variable resistor also known as a potentiometer or as a “pot” can also be used to control the potential or as a “pot” can also be used to control the potential difference across some device.difference across some device.

PotentiometerPotentiometer

Pots have a rotating wheel mounted in plastic and they are Pots have a rotating wheel mounted in plastic and they are commonly used as volume and tone controls in sound systems. commonly used as volume and tone controls in sound systems. They can be made from wire, metal oxides or carbon compounds.They can be made from wire, metal oxides or carbon compounds.

Sliding contact A can connect anywhere from one end Sliding contact A can connect anywhere from one end to the other of the resistor chain. This way it can to the other of the resistor chain. This way it can control voltage across a device and therefore the control voltage across a device and therefore the current through it, from maximm down to zero. current through it, from maximm down to zero.

1. step is to do a circuit without device and then adjust 1. step is to do a circuit without device and then adjust point A in such a way that there is no current passing through potentiometer. point A in such a way that there is no current passing through potentiometer.

Potential difference across potentiometer is 6 V.Potential difference across potentiometer is 6 V.

For some other battery point A would be somewhere else. If you include a lamp For some other battery point A would be somewhere else. If you include a lamp into circuit and the pointer is at A, potential difference across the lamp is zero.into circuit and the pointer is at A, potential difference across the lamp is zero. However, if the pointer is moved up to two-thirds the length of the potentiometer However, if the pointer is moved up to two-thirds the length of the potentiometer as in the figure, then the output voltage across the filament lamp would beas in the figure, then the output voltage across the filament lamp would be

⅔ ⅔ × 6V = 4V.× 6V = 4V.