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CHAPTER EIGHT
CURRENT ELECTRICITY
Electric Current
Electric current is the flow (movement) of electric charge. The SI
unit of electric current is the ampere, and electric current is
measured using an ammeter. The electric charge may be either
electrons or ions. The nature of the electric current is basically the
same for either type.
A solid conductive metal contains a large population
of mobile, or free, electrons. These electrons are
bound to the metal lattice but not to any individual
atom. Even with no external electric field applied,
these electrons move about randomly due to thermal
energy but, on average, there is zero net current
within the metal.
When a metal wire is connected across the two terminals of a DC
voltage source such as a battery, the source places an electric field
across the conductor.
The moment contact is made, the free electrons of the conductor are
forced to drift toward the positive terminal under the influence of
this field. The free electrons are therefore the current carrier in a
typical solid conductor.
For an electric current of 1 ampere, 1 coulomb of electric charge
(which consists of about 6.242 × 10exp18 electrons) drifts every
second through any plane through which the conductor passes.
Current density
Current density is a measure of the density of electric current. It is
defined as a vector whose magnitude is the electric current per
cross-sectional area. In SI units, the current density is measured in
amperes per square meter.
The drift speed of electric charges
Mobile charged particles within a conductor move constantly in
random directions, like the particles of a gas.
In order for there to be a net flow of charge, the particles must also
move together with an average drift rate.
Electrons are the charge carriers in metals and they follow an erratic
path, bouncing from atom to atom, but generally drifting in the
direction of the electric field.
The speed at which they drift can be calculated from the equation: 8. where I is the electric current n is number of charged particles per unit volume A is the cross-sectional area of the conductor v is the drift velocity, and Q is the charge on each particle.
The ratio of the speed of the electromagnetic wave to the speed of
light in free space is called the velocity factor, and depends on the
electromagnetic properties of the conductor and the insulating
materials surrounding it, and on their shape and size.
Resistance
If two or more circuit components are connected end to end like a
daisy chain, it is said they are connected in series. A series circuit
provides a single path for electric current through all of its
components.
If two or more circuit components are connected like the rungs of a
ladder it is said they are connected in parallel. A parallel circuit
provides separate paths for current through each of its components.
A parallel circuit provides the same voltage across all its components.
A series circuit is a circuit in which resistors are arranged in a chain,
so the current has only one path to take. The current is the same
through each resistor. The total resistance of the circuit is found by
simply adding up the resistance values of the individual resistors, so
the equivalent resistance of resistors in series is
Series circuits
Parallel circuits
A parallel circuit is a circuit in which the resistors are arranged with
their heads connected together, and their tails connected together.
The current in a parallel circuit breaks up, with some flowing along
each parallel branch and re-combining when the branches meet
again. The voltage across each resistor in parallel is the same.
The equivalent resistance of resistors in parallel is: 8.
In this case the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance. If the values of the three resistors are: The total resistance is found by This gives With a 10 V battery, by V = I R the total current in the circuit is: .
Circuits with series and parallel components
General rules for doing the reduction process include:
1. Two (or more) resistors with their heads directly connected
together and their tails directly connected together are in
parallel, and they can be reduced to one resistor using the
equivalent resistance equation for resistors in parallel.
2. Two resistors connected together so that the tail of one is
connected to the head of the next, with no other path for the
current to take along the line connecting them, are in series and can
be reduced to one equivalent resistor.
Finally, remember that for resistors in series, the current is the
same for each resistor, and for resistors in parallel, the voltage is
the same for each one.
Ohm’s Law
Ohm's law applies to electrical circuits; it states that the current
through a conductor between two points is directly proportional to
the potential difference (i.e. voltage drop or voltage) across the two
points, and inversely proportional to the resistance between them.
The resistance of most resistive devices (resistors) is constant over a
large range of values of current and voltage. When a resistor is used
under these conditions, the resistor is referred to as an ohmic device
(or an ohmic resistor) because a single value for the resistance
suffices to describe the resistive behavior of the device over the
range.
When sufficiently high voltages are applied to a resistor, forcing a
high current through it, the device is no longer ohmic because its
resistance, when measured under such electrically stressed
conditions, is different (typically greater) from the value measured
under standard conditions (see temperature effects, below).
Physicists often use the continuum form of Ohm's Law:
where J is the current density (current per unit area, unlike the simpler I, units of amperes, of Ohm's law), σ is the conductivity and E is the electric field (units of volts per meter, unlike the simpler V, units of volts, of Ohms's law).
The electrical resistance of a conductor is defined in terms of conductivity, length, and cross sectional area: 8.
Temperature effects
Over a limited temperature range, the resistivity of a metal varies approximately linearly with temperature according to the expression 8.
where ρ is the resistivity at some temperature T (in degrees Celsius), ρ 0 is the resistivity at some reference temperature T 0 (usually taken to be room temperature of 20 0 C), and α is the temperature coefficient of resistivity. From Equation 8. 15 the temperature coefficient of resistivity can be expressed as 8. where is the change in the resistivity in the temperature interval.
