5: Electric Current
5.1 Electric potential difference,
current and resistance
Electric Circuits
Q. Describe, in as much scientific detail
as possible, what happens in an electric
circuit when it is switched on.
The instant a circuit is turned on, an electrical field
develops (moving through the circuit at about the
speed of light). The field acts upon charged bodies.
Thus the free electrons in a wire (or other charge
carriers e.g. ions in liquids) begin to move almost
simultaneously and reach speeds up to 1/1000 x
speed of light. Constant interactions (collisions)
with atoms reduce the average speed of electrons
in a wire to around 0.5mms-1.
Energy and Work in Circuits
In any electrical circuit energy is transferred from
the power source (e.g. a cell or dynamo) to
somewhere else (e.g. to internal energy in a heating
element).
Q. In a simple torch circuit, describe the energy changes
occurring and describe what is doing the work and what is
having work done upon it.
Work is done by the cell on the electrons: the electric field
exerts a force upon them that makes them move through a
distance. The electrons interact with and do work upon the
atoms in the lamp filament, causing them to vibrate more.
Chemical energy → Kinetic energy → Internal energy
(in cells)
(of electrons)
(of filament)
Voltage
Voltage can be thought of as a sort of electrical
‘push’. Voltage at a point is also called ‘potential’
and can be measured at any point relative to
another point. Thus the ‘voltage across’ a
component is better described as the ‘potential
V2
V3
difference’.
EMF
+
V1
V2
V4
V1
V3
V4
EMF
Potential
• Voltage at a point is called the point potential.
• Point potential is always measured relative to
other points. E.g. the negative terminal of a cell or
Earth can be taken as zero.
• Potential difference can then be determined from
individual point potentials.
E.g.
If the potential at point A is 3.2V and point B is 1.2V what are
the potential differences across R, M and L? Sketch the
potential - position graph:
M
R
A
potential
(V)
B
L
4.5V
+
A
B
-
Potential Difference
This can be defined as follows:
The potential difference between any two points
in an electrical circuit is equal to the work done
moving one coulomb of charge from one point to
the other.
Potential difference =
V =
Work
Charge
W
Q
V = potential difference between
two points in the circuit (Volts)
W = work done (Joules)
Q = charge (Coulombs)
Electrical potential energy
So as an electron moves between two
points in a circuit, its potential energy will
decrease and its kinetic energy will
increase (ignoring collisions with atoms)
by an amount equal to the work done by
the electric field. So…
+
W = QV
∆KE = ∆PE = qV
∆E = change in energy(Joules)
V = potential difference (Volts)
q = charge of particle (Coulombs)
Q. Calculate the potential energy lost by an electron as it
moves from the negative to positive terminal of a 9 Volt
cell. What happens to this energy? (e = - 1.6 x 10-19 C)
The Electronvolt
When we are considering individual charged
particles gaining or losing energy, a typical order of
magnitude is 10-18 Joules. Clearly the Joule is a
cumbersome unit to use in this context. Instead we
use another unit of energy - the electronvolt.
One electronvolt (1eV) is the work done moving one
electron through a potential difference of one volt.
So…
W = QV
1eV = (-1.6 x 10-19) x -1
1eV = 1.6 x 10-19J
Electric current
Demo: The shuttling ball
This demonstration shows that…
…electric current is the rate of flow of charge.
One coulomb passes a point in a circuit when a current of
one amp flows for one second.
So…
ΔQ = I Δt
ΔQ = Charge (Coulombs)
I = Current (Amps)
Δt = Time taken (seconds)
Q. From the shuttling ball demo, determine the…
• Number of coulombs flowing per second
• Number of electrons flowing per second
• Charge on the ball
Amp-hours
A larger unit of charge, used in industrial and
engineering applications is the Amp-hour (Ah).
E.g. A 1.6 Ah cell can supply a current of 1.6A for
one hour.
Q1. Determine the charge stored in…
a. A 2.4 Ah camcorder battery
8640 C
b. A 700 mAh mobile phone battery 2520 C
c. A 60 Ah battery for a lorry
2.16 x 105 C
Q2.
Find the total charge delivered by a car battery
when current varies with use as shown.
Defining the Ampere
Demo: Force between two parallel wires
One ampere is defined as the current which will
produce an attractive force of 2×10–7 Newton per
metre of length between two straight, parallel
conductors (of infinite length and negligible circular
cross section) placed one metre apart.
Resistance
Resistance can be thought of as the opposition to
flow of charge in a conductor.
Resistance can be defined as the ratio of the
potential difference across the conductor to the
current flowing through it.
Thus…
R= V
I
R = Resistance (Ohms)
V = P.d. (Volts)
I = Current (Amps)
Factors affecting resistance
Experiment: Investigate the effect of length and
cross sectional area of a wire upon its resistance.
Use a similar circuit to this or an
Ohmmeter to determine the
relationships between…
A
a. Length and R
b. Cross sectional area and
resistance.
V
Results
R
R
length
R
area
1 / area
Resistivity
The resistance of a wire is proportional to its length
and inversely proportional to its cross sectional
area.
The resistance also depends upon the material
which has a certain resistivity (ρ).
Resistance = resistivity x length
cross sectional area
R = ρl
A
Can you determine a
unit for resistivity?
R = Resistance (Ω)
l = Length of conductor (m)
A = cross sectional area (m2)
ρ = resistivity (Ωm)
E.g.
The live rail of an electric railway has a c.s. area of
50cm2. The resistivity of steel is 1.0 x 10-7 Ωm.
Ignoring the resistive effects of joints, determine the
resistance per km.
Strain Gauges
Engineers use strain gauges to
measure strain magnitude and
distribution in structures, aircraft,
bridges etc. (High strain regions can
lead to failure).
It is designed as a long wire folding
back upon itself and is stuck onto
surfaces.
Q. What will happen to the
resistance when the surface bends.
Why?
Ohm’s Law
If an electrical conductor obeys Ohm’s law then…
… the current flowing through the
conductor is directly proportional to
the potential difference across the
conductor (so long as temperature is
constant).
V
I
An Ohmic conductor has a constant ratio between
the voltage and current. i.e. its resistance is
constant.
E.g. A carbon resistor is an
Ohmic conductor.
Electrical Power
Experiment: To determine the power of a lamp.
1. Measure I and V
A
V
2. Determine the charge that
passes through the lamp in
one minute
3. Determine the work done by
the cell on the charge and
lamp in one minute.
4. Now determine the work done
in one second. What have
you calculated?
We know…
V =
so…
W = QV
but…
Q = It and
P = ItV
t
so…

W
Q
P= W
t
P = IV
Note: For a resistor, substituting V = IR into P = IV
gives…
Power dissipated = I2R
or P = V2
R
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