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.

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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.
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?

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
(joules) (coulombs)

x p.d.., V
(volts)
The Electronvolt
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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.

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 = Δq/ Δt
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.

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Resistance is measured in ohms (Ω) and is defined
in the following way:
–
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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.

Ohm’s 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.
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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.

When X is a filament lamp, the graph
is a curve, as shown:
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.
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Power Dissipation
Electric Circuits
Topic 5.2 Electric Circuits
Electromotive Force
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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
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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?
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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.
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Resistance Combinations
Resistors in series
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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:
–
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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 = IRl+IR2+IR3
If we now divide each term in the equation by I,
we get:
–
R = R1 + R2 + R 3
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 + I 2 + I 3
the combined resistance R is calculated from the
equation:
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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 = I1+I2+I3
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 get:V/R=V/R1 + V/R2 + V/R3
Now we divide each term by V, to get:
1
1
1
1

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R R1 R2 R3
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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 Ω.

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 MΩ, 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
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Using Ohm’s 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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