11. Charge and Current11. Charge and Current11. Charge and Current11. Charge and Current

CurrentCurrentCurrentCurrent

CurrentCurrentCurrentCurrent is the rate of flow of charge (i.e. the amount of charge flowing past a point

per second).

If a charge of Coulombs flow past a point in a time , then the current is:

=

Current is measured in amperes (A). 1 C s-1 = 1 A.

Drift VelocityDrift VelocityDrift VelocityDrift Velocity

Current is carried by the movement of charge carriers (e.g. free electrons, ions).

In a conductor, the free electrons act as charge carriers. These constantly collide with

positive ions, causing the electrons to move about randomly. When a potential

difference is applied, the electrons continue to move randomly, but there will be a

small net motion ("drift") towards one side because of the electrostatic force exerted

on them by the electric field.

The speed of this net movement of electrons is called the drift velocitydrift velocitydrift velocitydrift velocity (). Unit: m s-1

Charge carrier densityCharge carrier densityCharge carrier densityCharge carrier density: the number of charge carriers per cubic metre of the material

(). Unit: m-3

If the charge carrier in the material has a charge

the current is given by:

Charge is quantisedquantisedquantisedquantised. Generally, we get negative charge on objects when it has excess

electrons, and a positive charge when it has excess protons. Protons and electrons

have the same sizes of charge. So generally, "charged" objects

whole number multiple of the charge of an electron (

By convention, the direction of current is defined as the direction of flow of positive

charge. If current is carried by electrons, the

direction opposite to the flow of electrons.

Metals have charge carrier densities of order 10

no free charge carriers near room temperature. At room temperature, semiconductors

typically have charge carrier densities 10

Typically, drift speeds are quite slow, but a light would light up as soon as you turn

the switch on because the

speed of light and so electrons in all parts of the wire begin to move under the effect

of this field almost immediately after the switch is turned on

To show that drift speeds are slow, the following experimen

If the charge carrier in the material has a charge and a cross-sectional area

=

. Generally, we get negative charge on objects when it has excess

electrons, and a positive charge when it has excess protons. Protons and electrons

have the same sizes of charge. So generally, "charged" objects have a charge that is a

whole number multiple of the charge of an electron ( = 1.610-19 C).

By convention, the direction of current is defined as the direction of flow of positive

carried by electrons, the conventional current woul

direction opposite to the flow of electrons.

Metals have charge carrier densities of order 1028 - 1029 m-3. Insulators have almost

no free charge carriers near room temperature. At room temperature, semiconductors

carrier densities 1017 - 1019.

Typically, drift speeds are quite slow, but a light would light up as soon as you turn

the electric field that causes electrons to move travel at the

speed of light and so electrons in all parts of the wire begin to move under the effect

almost immediately after the switch is turned on.

To show that drift speeds are slow, the following experiment could be carried out:

sectional area , then

. Generally, we get negative charge on objects when it has excess

electrons, and a positive charge when it has excess protons. Protons and electrons

have a charge that is a

C).

By convention, the direction of current is defined as the direction of flow of positive

would run in the

. Insulators have almost

no free charge carriers near room temperature. At room temperature, semiconductors

Typically, drift speeds are quite slow, but a light would light up as soon as you turn

that causes electrons to move travel at the

speed of light and so electrons in all parts of the wire begin to move under the effect

t could be carried out:

Common Common Common Common Circuit SymbolsCircuit SymbolsCircuit SymbolsCircuit Symbols

12121212.... Potential Difference, Electromotive Force Potential Difference, Electromotive Force Potential Difference, Electromotive Force Potential Difference, Electromotive Force

and Powerand Powerand Powerand Power

The electrons that flow in a circuit have electrical energy. As they travel around the

circuit, the electric energy is converted to other forms.

Potential differencePotential differencePotential differencePotential difference between two points in the circuit is the amount of electrical

energy converted into other forms per Coulomb of charge as it flows between the

points. In other words, potential difference is the work done per Coulombthe work done per Coulombthe work done per Coulombthe work done per Coulomb.

If a charge does amount of work as it moves between two points in the circuit,

then the potential difference is given by:

=

Potential difference is measured in Volts (V). 1 V = 1 J C-1.

The electrical energy given to a Coulomb of charge as it moves through a cell or

generator is called the electromotive force (emf)electromotive force (emf)electromotive force (emf)electromotive force (emf) (((()))). Here, another form of energy is

being converted into electrical energy. For instance, a cell converts chemical energy to

electrical energy. We can write:

=

Emf is measured in Volts (V). 1 V = 1 J C-1.

PowerPowerPowerPower

PowerPowerPowerPower is the rate of work donerate of work donerate of work donerate of work done or work done per second. If in a time of , amount of

work is done, then power is:

=

= so if we divide both sides by , on LHS you get

= and on RHS you have

= . Combining the two, we get an important equation that tells us the power in

terms of potential difference and the current :

=

Power is the work done per second. If you want to find the total work done (or the

total energy converted) during a time period of , you need to multiply power by the

time:

= =

13. Current13. Current13. Current13. Current----Potential Difference RelationshipsPotential Difference RelationshipsPotential Difference RelationshipsPotential Difference Relationships

Rheostats can be used to vary either the current in a circuit or the potential

difference across two terminals in a circuit.

detail later.

Using a rheostat, an ammeter and a voltmeter, it is possible to investigate how the

current across a piece of conductor changes as the potent

changed. We will investigate the relationships for metallic conductors,

filament lamps as well as semiconductor diodes.

IIII----V Characteristics for a Metallic ConductorV Characteristics for a Metallic ConductorV Characteristics for a Metallic ConductorV Characteristics for a Metallic Conductor

To investigate how the current in a metallic conductor changes as you change the

potential difference across it, you can carry out the experiment

A graph of current vs. voltage ("an I

follows:

Potential Difference RelationshipsPotential Difference RelationshipsPotential Difference RelationshipsPotential Difference Relationships

Rheostats can be used to vary either the current in a circuit or the potential

difference across two terminals in a circuit. We will look at these in a little more

Using a rheostat, an ammeter and a voltmeter, it is possible to investigate how the

current across a piece of conductor changes as the potential difference across it is

ed. We will investigate the relationships for metallic conductors,

filament lamps as well as semiconductor diodes.

V Characteristics for a Metallic ConductorV Characteristics for a Metallic ConductorV Characteristics for a Metallic ConductorV Characteristics for a Metallic Conductor

current in a metallic conductor changes as you change the

potential difference across it, you can carry out the experiment below

A graph of current vs. voltage ("an I-V graph") from this experiment will look as

Potential Difference RelationshipsPotential Difference RelationshipsPotential Difference RelationshipsPotential Difference Relationships

Rheostats can be used to vary either the current in a circuit or the potential

We will look at these in a little more

Using a rheostat, an ammeter and a voltmeter, it is possible to investigate how the

ial difference across it is

ed. We will investigate the relationships for metallic conductors, tungsten

current in a metallic conductor changes as you change the

below:

V graph") from this experiment will look as

The current is proportional to the potential difference, and this is stated in Ohm's lawOhm's lawOhm's lawOhm's law

as follows: "for a metal at constant temperature, the current in thfor a metal at constant temperature, the current in thfor a metal at constant temperature, the current in thfor a metal at constant temperature, the current in the metal is directly e metal is directly e metal is directly e metal is directly

proportional to the potential difference across itproportional to the potential difference across itproportional to the potential difference across itproportional to the potential difference across it". A conductor obeying this law is

called an "Ohmic ConductorOhmic ConductorOhmic ConductorOhmic Conductor".

ResistanceResistanceResistanceResistance is a property of a conductor that measures the conductor's opposition to a

current flowing in it.

A conductor is made of many lattice ions, which are surrounded by a "sea" of unbound

"delocalised" electrons. It is these delocalised electrons that flow to produce a current.

When lattice ions vibrate, they can knock the conducting electrons off their path.

This is how there is an opposition to the flow of current.

Resistance () is defined as:

=

where is the potential difference in the conductor (in Volts), and is the current in the

conductor (in Amperes). Resistance is measured in Ohms, and it has the symbol .

Generally, this is relationship is remembered as

=

The resistance of an Ohmic conductor is constant, so if you draw a graph of its

resistance () against voltage (), you get a flat line:

IIII----V Characteristics for a Tungsten Filament LampV Characteristics for a Tungsten Filament LampV Characteristics for a Tungsten Filament LampV Characteristics for a Tungsten Filament Lamp

You can use the setup shown

changes as potential difference across it

The I-V graph for this experiment looks as

In this case, as the potential difference is increased and more current flows in the

conductor, the wire heats

amplitudes. The collision rate of lattice ions

which means the resistance of the filament increases.

continues to rise when you increase the potential difference, this rate of rise will

decrease.

Note: An INote: An INote: An INote: An I----V curve that gets V curve that gets V curve that gets V curve that gets

The resistance () against voltage (

there is a resistance even when there is no p.d. across the filament

V Characteristics for a Tungsten Filament LampV Characteristics for a Tungsten Filament LampV Characteristics for a Tungsten Filament LampV Characteristics for a Tungsten Filament Lamp

You can use the setup shown below to investigate how the current of a filament lamp

changes as potential difference across it is changed.

V graph for this experiment looks as follows:

In this case, as the potential difference is increased and more current flows in the

heats up and this causes the lattice atoms to vibrate

collision rate of lattice ions with conducting electrons increases,

which means the resistance of the filament increases. So even though the current

continues to rise when you increase the potential difference, this rate of rise will

V curve that gets V curve that gets V curve that gets V curve that gets flatter indicates an increasing flatter indicates an increasing flatter indicates an increasing flatter indicates an increasing resistance.resistance.resistance.resistance.

against voltage () graph for a filament looks as follows

there is a resistance even when there is no p.d. across the filament:

to investigate how the current of a filament lamp

In this case, as the potential difference is increased and more current flows in the

the lattice atoms to vibrate with larger

conducting electrons increases,

So even though the current

continues to rise when you increase the potential difference, this rate of rise will

resistance.resistance.resistance.resistance.

graph for a filament looks as follows. Note that

IIII----V CV CV CV Chhhharactearactearactearacteristics for an NTC Thermistorristics for an NTC Thermistorristics for an NTC Thermistorristics for an NTC Thermistor

You can use the setup shown below to investigate how the current across an NTC

thermistor changes as potential difference across it is changed.

The resulting vs. graph has the following shape:

As the current flows across the NTC thermistor, it heats up. This causes two things:

o TTTThe lattice ions vibrate with larger amplitudeshe lattice ions vibrate with larger amplitudeshe lattice ions vibrate with larger amplitudeshe lattice ions vibrate with larger amplitudes. Just like with the filament

lamp, their vibrations knock off conducting electrons. So reduces the drift

velocity of conduction electrons. This contributes to raise the resistance.

o Electrons which are bonded to atoms gain enough energy to break freeElectrons which are bonded to atoms gain enough energy to break freeElectrons which are bonded to atoms gain enough energy to break freeElectrons which are bonded to atoms gain enough energy to break free of their

atoms and they become free electrons. So the charge carrier density increases.

This contributes to lower the resistance.

From these two phenomena, the rise in the charge carrier densityrise in the charge carrier densityrise in the charge carrier densityrise in the charge carrier density has a much larger has a much larger has a much larger has a much larger

effect on the resistance. So effect on the resistance. So effect on the resistance. So effect on the resistance. So overall, overall, overall, overall, the resistance of the NTC thermistor decreasesthe resistance of the NTC thermistor decreasesthe resistance of the NTC thermistor decreasesthe resistance of the NTC thermistor decreases,

causing the current to rise at an increasing rate.

Note: An Note: An Note: An Note: An ---- curve that gets steepercurve that gets steepercurve that gets steepercurve that gets steeper indicates a decreasing resistanceindicates a decreasing resistanceindicates a decreasing resistanceindicates a decreasing resistance.

So in a NNNNegativeegativeegativeegative TTTTemperature emperature emperature emperature CCCCoefficient (NTC) thermistor, resistance increases as oefficient (NTC) thermistor, resistance increases as oefficient (NTC) thermistor, resistance increases as oefficient (NTC) thermistor, resistance increases as

the temperature increases.the temperature increases.the temperature increases.the temperature increases. "Negative" here indicates that as temperature rises,

resistance falls. This is in contrast to positive temperature coefficient (PTC)

materials, where an increased temperature causes the resistance to increase as well.

Investigating the change in

This is essentially the same as the experiment

more details regarding the experiment's setup (important

The setup is as follows:

Insert the thermistor into a beaker containing crushed ice.

Start the Bunsen burner (

3! Sometimes they won't give marks for just

raise the temperature.

At regular time intervals, note down

corresponding resistance

reaches the boiling point.

Plot a graph of resistance

Precautions to ensure accuracy:

o Before taking a reading, remove the flame from under the beaker and stir th

water well for a little while. This ensures that the water has uniform

temperature throughout and that the thermistor has had enough time to come

to thermal equilibrium

sides of the beaker,

o When taking readings

reading, in order to avoid parallax errors.

Investigating the change in resistance in an NTC Thermistor with temperature

This is essentially the same as the experiment we discussed above, but we will go into

more details regarding the experiment's setup (important for unit 3)

Insert the thermistor into a beaker containing crushed ice.

Start the Bunsen burner (show this in your diagram if you're asked to do this in

give marks for just an arrow labelled "heat"!)

, note down the temperature in the water bath

resistance of the thermistor (using the ohmmeter). Do this until water

Plot a graph of resistance vs. temperature, which should look like this

Precautions to ensure accuracy:

Before taking a reading, remove the flame from under the beaker and stir th

water well for a little while. This ensures that the water has uniform

temperature throughout and that the thermistor has had enough time to come

equilibrium with water. Do not allow the thermome

sides of the beaker, and keep it close to the thermistor.

en taking readings of temperature, ensure the eye is in line with the

reading, in order to avoid parallax errors.

rmistor with temperature

but we will go into

unit 3)

in your diagram if you're asked to do this in unit

an arrow labelled "heat"!) and slowly

in the water bath and the

Do this until water

this:

Before taking a reading, remove the flame from under the beaker and stir the

water well for a little while. This ensures that the water has uniform

temperature throughout and that the thermistor has had enough time to come

water. Do not allow the thermometer to touch the

temperature, ensure the eye is in line with the

Other sources of systematic uncertainties (not discussed above):

o It is not possible to simultaneously read temperature and resistance. After the

temperature is read, a short time will elapse before resistance can be read.

Using a datalogger would remove this uncertainty.

o Zero errors on the ohmmeter.

Safety precautions:

o The water will be very hot so avoid touching it.

o Do not over-fill the beaker and ensure that the water does not boil and spill

over. When not taking readings, stand away from the beaker to avoid getting

hot water splashed.

o The wires may get hot so avoid touching them.

Note that we are using an ohmmeter to measure resistance, not a voltmeter/ammeter

combination. Using an ohmmeter is advantageous because you can directly read off

the resistance from the ohmmeter. This means:

o Just having to read two measurements rather than three has less uncertainty

than having to take three simultaneous readings

o The uncertainty in the ohmmeter reading is likely smaller than the combined

uncertainties in the voltmeter and ammeter

But even if you do it with a voltmeter and ammeter method, you won't lose any marks.

IIII----V Characteristics for a V Characteristics for a V Characteristics for a V Characteristics for a

You can use the setup below

potential difference across it is changed.

Diodes can be connected to a circuit either in

connected in forward biasforward biasforward biasforward bias

conventional current (+ve to

forward bias, the one on the right is connected in reverse bias.

When a diode is connected in reverse bias,

and current cannot flow through it. It can

forward bias.

V Characteristics for a V Characteristics for a V Characteristics for a V Characteristics for a Semiconductor DiodeSemiconductor DiodeSemiconductor DiodeSemiconductor Diode

low to investigate how the current in a diode varies as the

potential difference across it is changed.

Diodes can be connected to a circuit either in forward biasforward biasforward biasforward bias or in reverse biasreverse biasreverse biasreverse bias

forward biasforward biasforward biasforward bias, the "arrow" of the diode symbol points in the direction of

conventional current (+ve to -ve potential). The diagram on the left is conneced in

forward bias, the one on the right is connected in reverse bias.

When a diode is connected in reverse bias, it offers a very large ("infinite") resistance

current cannot flow through it. It can conduct current when it is connected in

to investigate how the current in a diode varies as the

reverse biasreverse biasreverse biasreverse bias. When

ts in the direction of

ve potential). The diagram on the left is conneced in

it offers a very large ("infinite") resistance

conduct current when it is connected in

The I-V graph for the semiconductor diode looks as

The diode will not conduct current when it is connected in reverse bias, and it will

take a certain voltage in the forward direction for it to start conducting current.

is called the cutcutcutcut----in voltagein voltagein voltagein voltage

LightLightLightLight----Dependent ResistorsDependent ResistorsDependent ResistorsDependent Resistors

A light-dependent resistor (LDR) is a device whose resistance

intensity of light that falls on it

symbol for an LDR is:

A typical resistance vs. light intensity graph looks as follows:

V graph for the semiconductor diode looks as follows:

The diode will not conduct current when it is connected in reverse bias, and it will

voltage in the forward direction for it to start conducting current.

in voltagein voltagein voltagein voltage and it is typically about 0.5 V.

Dependent ResistorsDependent ResistorsDependent ResistorsDependent Resistors

dependent resistor (LDR) is a device whose resistance decreases

intensity of light that falls on it increases (i.e. brighter light, less resistance)

A typical resistance vs. light intensity graph looks as follows:

The diode will not conduct current when it is connected in reverse bias, and it will

voltage in the forward direction for it to start conducting current. This

decreases when the

(i.e. brighter light, less resistance). The