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Electric Currents

- Topic 5.1 Electric potential difference, current

and resistance

Electric Potential Energy

- If you want to move a charge closer to a charged

sphere you have to push against the repulsive

force - You do work and the charge gains electric

potential energy. - If you let go of the charge it will move away

from the sphere, losing electric potential

energy, but gaining kinetic energy.

- When you move a charge in an electric field its

potential energy changes. - This is like moving a mass in a gravitational

field.

- The electric potential V at any point in an

electric field is the potential energy that each

coulomb of positive charge would have if placed

at that point in the field. - The unit for electric potential is the joule per

coulomb (J C-1), or the volt (V). - Like gravitational potential it is a scalar

quantity.

- In the next figure, a charge q moves between

points A and B through a distance x in a uniform

electric field. - The positive plate has a high potential and the

negative plate a low potential. - Positive charges of their own accord, move from a

place of high electric potential to a place of

low electric potential. - Electrons move the other way, from low potential

to high potential.

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- In moving from point A to point B in the diagram,

the positive charge q is moving from a low

electric potential to a high electric potential. - The electric potential is therefore different at

both points.

- In order to move a charge from point A to point

B, a force must be applied to the charge equal to

qE - (F qE).
- Since the force is applied through a distance x,

then work has to be done to move the charge, and

there is an electric potential difference between

the two points. - Remember that the work done is equivalent to the

energy gained or lost in moving the charge

through the electric field.

Electric Potential Difference

- Potential difference
- We often need to know the difference in potential

between two points in an electric field - The potential difference or p.d. is the energy

transferred when one coulomb of charge passes

from one point to the other point.

- The diagram shows some values of the electric

potential at points in the electric field of a

positively-charged sphere - What is the p.d. between points A and B in the

diagram?

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- When one coulomb moves from A to B it gains 15 J

of energy. - If 2 C move from A to B then 30 J of energy are

transferred. In fact

Change in Energy

- Energy transferred,
- This could be equal to the amount of electric

potential energy gained or to the amount of

kinetic energy gained - W charge, q x p.d.., V
- (joules) (coulombs) (volts)

The Electronvolt

- One electron volt (1 eV) is defined as the energy

acquired by an electron as a result of moving

through a potential difference of one volt. - Since W q x V
- And the charge on an electron or proton is 1.6 x

10-19C - Then W 1.6 x 10-19C x 1V
- W 1.6 x 10-19 J
- Therefore 1 eV 1.6 x 10-19 J

Conduction in Metals

- A copper wire consists of millions of copper

atoms. - Most of the electrons are held tightly to their

atoms, but each copper atom has one or two

electrons which are loosely held. - Since the electrons are negatively charged, an

atom that loses an electron is left with a

positive charge and is called an ion.

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- The diagram shows that the copper wire is made up

of a lattice of positive ions, surrounded by

free' electrons - The ions can only vibrate about their fixed

positions, but the electrons are free to move

randomly from one ion to another through the

lattice. - All metals have a structure like this.

What happens when a battery is attached to the

copper wire?

- The free electrons are repelled by the negative

terminal and attracted to the positive one. - They still have a random movement, but in

addition they all now move slowly in the same

direction through the wire with a steady drift

velocity. - We now have a flow of charge - we have electric

current.

Electric Current

- Current is measured in amperes (A) using an

ammeter. - The ampere is a fundamental unit.
- The ammeter is placed in the circuit so that the

electrons pass through it. - Therefore it is placed in series.
- The more electrons that pass through the ammeter

in one second, the higher the current reading in

amps.

- 1 amp is a flow of about 6 x 1018 electrons in

each second! - The electron is too small to be used as the basic

unit of charge, so instead we use a much bigger

unit called the coulomb (C). - The charge on 1 electron is
- only 1.6 x 10-19 C.

- In fact

Or I ?q/ ?t Current is the rate of flow of

charge

- Which way do the electrons move?
- At first, scientists thought that a current was

made up of positive charges moving from positive

to negative. - We now know that electrons really flow the

opposite way, but unfortunately the convention

has stuck. - Diagrams usually show the direction of

conventional current' going from positive to

negative, but you must remember that the

electrons are really flowing the opposite way.

Resistance

- A tungsten filament lamp has a high resistance,

but connecting wires have a low resistance. - What does this mean?
- The greater the resistance of a component, the

more difficult it is for charge to flow through

it.

- The electrons make many collisions with the

tungsten ions as they move through the filament. - But the electrons move more easily through the

copper connecting wires because they make fewer

collisions with the copper ions.

- Resistance is measured in ohms (O) and is defined

in the following way - The resistance of a conductor is the ratio of the

p.d. applied across it, to the current passing

through it. - In fact

Resistors

- Resistors are components that are made to have a

certain resistance. - They can be made of a length of nichrome wire.
- Nichrome wire is a nickel-chromium mixture.

Ohms Law

- The current through a metal wire is directly

proportional to the p.d. across it (providing the

temperature remains constant). - This is Ohm's law.
- Materials that obey Ohm's law are called ohmic

conductors.

Ohmic and Non-Ohmic Behavior

- What do the current-voltage graphs tell us?

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- When X is a metal resistance wire the graph is a

straight line passing through the origin (if the

temperature is constant) - This shows that I is directly proportional to V.
- If you double the voltage, the current is doubled

and so the value of V/I is always the same. - Since resistance R V/I, the wire has a constant

resistance. - The gradient is the resistance on a V against I

graph, and 1/resistance in a I against V graph.

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- When X is a filament lamp, the graph is a curve,

as shown

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- Doubling the voltage produces less than double

the current. - This means that the value of V/I rises as the

current increases. - As the current increases, the metal filament gets

hotter and the resistance of the lamp rises.

- The graphs for the wire and the lamp are

symmetrical. - The current-voltage characteristic looks the

same, regardless of the direction of the current.

Power Dissipation

Electric Circuits

- Topic 5.2 Electric Circuits

Electromotive Force

- Defining potential difference
- The coulombs entering a lamp have electrical

potential energy - those leaving have very little potential energy.
- There is a potential difference (or p.d.) across

the lamp, because the potential energy of each

coulomb has been transferred to heat and light

within the lamp. - p.d. is measured in volts (V) and is often called

voltage.

- The p.d. between two points is the electrical

potential energy transferred to other forms, per

coulomb of charge that passes between the two

points.

- Resistors and bulbs transfer electrical energy to

other forms, but which components provide

electrical energy? - A dry cell, a dynamo and a solar cell are some

examples. - Any component that supplies electrical energy is

a source of electromotive force or e.m.f. - It is measured in volts.
- The e.m.f. of a dry cell is 1.5 V, that of a car

battery is 12 V

- A battery transfers chemical energy to electrical

energy, so that as each coulomb moves through the

battery it gains electrical potential energy. - The greater the e.m.f. of a source, the more

energy is transferred per coulomb. In fact - The e.m.f of a source is the electrical potential

energy transferred from other forms, per coulomb

of charge that passes through the source. - Compare this definition with the definition of

p.d. and make sure you know the difference

between them.

Internal Resistance

- The cell gives 1.5 joules of electrical energy to

each coulomb that passes through it, - but the electrical energy transferred in the

resistor is less than 1.5 joules per coulomb and

can vary. - The circuit seems to be losing energy - can you

think where?

- The cell itself has some resistance, its internal

resistance. - Each coulomb gains energy as it travels through

the cell, but some of this energy is wasted or

lost' as the coulombs move against the

resistance of the cell itself. - So, the energy delivered by each coulomb to the

circuit is less than the energy supplied to each

coulomb by the cell.

- Very often the internal resistance is small and

can be ignored. - Dry cells, however, have a significant internal

resistance. - This is why a battery can become hot when

supplying electric current. - The wasted energy is dissipated as heat.

Resistance Combinations

Resistors in series

- The diagram shows three resistors connected in

series - There are 3 facts that you should know for a

series circuit - the current through each resistor in series is

the same - the total p.d., V across the resistors is the sum

of the p.d.s across the separate resistors, so V

Vl V2 V3 - the combined resistance R in the circuit is the

sum of the separate resistors

- R Rl R2 R3
- Suppose we replace the 3 resistors with one

resistor R that will take the same current I when

the same p.d. V is placed across it

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- This is shown in the diagram. Let's calculate R.
- We know that for the resistors in series
- V Vl V2 V3
- But for any resistor p.d. current x resistance

(V I R). - If we apply this to each of our resistors, and

remember that the current through each resistor

is the same and equal to I, we get - IR IRlIR2IR3
- If we now divide each term in the equation by I,
- we get
- R R1 R2 R3

Resistors in parallel

- We now have three resistors connected in

parallel - There are 3 facts that you should know for a

parallel circuit - the p.d. across each resistor in parallel is the

same - the current in the main circuit is the sum of the

currents in each of the parallel branches, so - I I1 I2 I3
- the combined resistance R is calculated from the

equation

- Suppose we replace the 3 resistors with one

resistor R that takes the same total current I

when the same p.d. V is placed across it.

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- This is shown in the diagram. Now let's

calculate R. - We know that for the resistors in parallel
- I I1I2I3
- But for any resistor, current p.d. resistance

(I V/R ). - If we apply this to each of our resistors, and

remember that the - p.d. across each resistor is the same and equal

to V, - we getV/RV/R1 V/R2 V/R3
- Now we divide each term by V, to get

- You will find that the total resistance R is

always less than the smallest resistance in the

parallel combination.

Circuit Diagrams

- You need to be able to recognize and use the

accepted circuit symbols included in the Physics

Data Booklet

Ammeters and Voltmeters

- In order to measure the current, an ammeter is

placed in series, in the circuit. - What effect might this have on the size of the

current? - The ideal ammeter has zero resistance, so that

placing it in the circuit does not make the

current smaller. - Real ammeters do have very small resistances -

around 0.01 O.

- A voltmeter is connected in parallel with a

component, in order to measure the p.d. across

it. - Why can this increase the current in the circuit?
- Since the voltmeter is in parallel with the

component, their combined resistance is less than

the component's resistance. - The ideal voltmeter has infinite resistance and

takes no current. - Digital voltmeters have very high resistances,

around 10 MO, and so they have little effect on

the circuit they are placed in.

Potential dividers

- A potential divider is a device or a circuit that

uses two (or more) resistors or a variable

resistor (potentiometer) to provide a fraction of

the available voltage (p.d.) from the supply.

- The p.d. from the supply is divided across the

resistors in direct proportion to their

individual resistances.

- Take the fixed resistance circuit - this is a

series circuit therefore the current in the same

at all points. - Isupply I1 I2
- Where I1 current through R1
- I2 current through R2

- Using Ohms Law

Example

With sensors

- A thermistor is a device which will usually

decrease in resistance with increasing

temperature. - A light dependent resistor, LDR, will decrease in

resistance with increasing light intensity.

(Light Decreases its Resistance).

Example

- Calculate the readings on the meters shown below

when the thermistor has a resistance of - a) 1 kW (warm conditions) and b) 16 kW. (cold

conditions)

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