Current and electric circuits
Chapter
4 1
Chapter
electric current
Electric current is an ordered motion of charges.
The direction of the current, for historical reasons,
is defined as opposite to the direction of motion of the electrons.
Electric current is the rate of flow of charge through a
conductor:
I
q
t
The unit of electric current
is the ampere, A:
The instantaneous current is given by:

1 A = 1 C/s
I
dq
dt
the battery
Volta discovered that a current
could be generated if different metals
were connected by a conductive solution
called an electrolyte.
A voltaic cell
A battery is a device that is capable
of transforming chemical energy
into electrical energy.
In cells, chemical reactions take place
that produce a potential difference
between the terminals.
This potential difference persists,
and the current is kept flowing,
until the reactions end.
a simple electric circuit
A complete circuit consist of multiple devices connected such that current
can flow all the way round the circuit.
A typical circuit
can be made of a battery,
connecting wires,
a switch and a light bulb,
or other device.
A hydraulic circuit can be seen as
analogous to an electrical circuit.
Flow of water
Valve
Water wheel
Resistance
Current
Switch
Ohm’s law
It is known from experiment that the current flowing
in an ohmic conductor is proportional
to the potential difference across it.
The constant of proportionality, R, is the called the resistance.
I

V
R
R

V
I
Resistance is a measure of how much a conductor
impedes the flow of current and in a circuit
it can be a device (like a bulb).
At the molecular level, electrons undergo frequent
collisions with the ions of materials.
The higher the number of collisions,
the higher the resistance of the material is.
The unit of resistance is the ohm, Ω: 1 Ω = 1 V/A.
idresistance and resistivity
The resistance in a conducting wire is proportional
to its length l and inversely proportional to its crosssectional area A:
l
A

Resistivity
ρ is characteristic of a material,and its value varies with temperature:
R 



 T  20C 1 T

The table below gives the resistivity and temperature coefficients (the relative change in resistivity
when the temperature is changed by 1 oC) of typical conductors and insulators.

material
resistivity (
m)
temperature coefficient,  (C°) 1
silver
1.59 x 10-8
0.0061
copper
1.68 x 10-8
0.0068
gold
2.44 x 10-8
0.0034
aluminium
2.65 x 10-8
0.00429
tungsten
5.60 x 10-8
0.0045
iron
9.71 x 10-8
0.00651
carbon
(3-60) x 10-5
-0.0005
silicon
(1.500) x 10-3
-0.05
109 - 1012
-
glass
resistors in series and in parallel
For resistors in series,
the current through
each resistor is the same.
The equivalent resistance
equals the sum
of each single
resistance.
For resistors in parallel,
the current is split into
different minor currents.
The inverse of the equivalent
resistance equals the sum
of the reciprocals
of the individual resistances.
1
1
1
1



R eq R1 R 2 R 3
R eq  R1  R 2  R 3


electric power
Electric power, as in dynamics, is the energy transformed by a device per unit time:
P
The unit of power is the watt,
 W.
U q

V
t
t
 P IV
For ohmic devices, we can make the following
substitutions:
 
P  IV  I IR  I 2R
V 
V2
P  IV   V 
R
R 
For example, the resistance
of a 40 W automobile headlight
designed for 12 V is
V2
R
 3.6 
P

In an electricity bill, what is reported,
is not the cost of power, but of energy:
thepower consumption multiplied by time.
Energy is measured in joules, but the electricity
supplier measures it in kilowatt-hours, kWh:
1 kWh = (1000 W) × (3600 s) = 3.60 x 106 J.
power in household circuits
The wires used in homes to carry electricity have very low resistances.
However, if the current is high enough, the power will increase and the wires can become hot enough
to start a fire.
To avoid this, fuses or circuit breakers are used,
which disconnect the supply when the current
drawn goes above a predetermined value.
When the current
exceeds
certain value,
the metallic ribbon
melts
and the circuit breaks.
The fuse must
then be replaced.
superconductivity
Some materials have
resistivity that suddenly
drops to zero when
the temperature is very low.
This temperature is called
the critical temperature Tc.
At T < Tc, a superconducting
material has zero resistivity.
At Tc, the resistivity
becomes non-zero and
increases with temperature
like other materials.
C
Experiments have shown that currents, once started, can flow through these materials
for years without decreasing, even in the absence of a potential difference.
In the Large Hadron Collider (LHC) at CERN
(European Organisation for Nuclear Research)
more then 1200 superconducting magnets are
used to bend the path of accelerating particle
beams and to keep them on course.