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CHAPTER 6 - ELECTRICITY AND MAGNETISM
Electric Charge and Current
All matter is made of positive particles called protons and
negative particles called electrons. In order to create an electric
charge, electrons must be separated from neutral atoms which
have an equal number of protons and electrons.
This results in two charges. The atoms which lost electrons are
now positive since they have more protons than electrons. The
electrons that have been removed give the object that removed
them a negative charge since it now has more electrons than
protons.
The third atomic particle we will discuss in more detail later is
the neutron which has no charge and has about the same mass
as a proton.
The unit of electric charge is called the coulomb. 6.25 x 1018
electrons or protons are contained in 1 coulomb of charge.
Electric current is defined as the time rate of flow of electric
charge. The equation used to calculate current is:
I = q/t
where I is current in amperes, q is amount of charge in
coulombs, and t is time in seconds. The basic unit of current,
ampere(A) is one coulomb per second. Sometimes ampere is
shortened to amp.
Example
Find the magnitude of the electric current if 4.8 x 1018 electrons
pass by a point in a wire during .25 seconds.
Currents flow easily through materials that are good
conductors. Good conductors have loosely bound electrons that
are able to move easily. Metals are good conductors since they
have electrons that are not bound to any one specific atom.
Materials in which nearly all of the electrons are tightly bound
are called insulators since they do not conduct electric currents
very well. Examples are wood, glass, and plastics.
Materials which are intermediate conductors(neither good nor
bad) are called semiconductors. Graphite and silicon are
examples.
Electric Force
Any two charged particles will exert an electric force on each
other. The nature of these forces is stated by the Law of
Charges:
Like charges repel, unlike charges attract.
Two negative charges or two positive charges repel each other.
A positive and negative charge will attract.
The magnitude of the electric force is determined by
Coulomb's Law.
The force between two charged bodies is directly
proportional to the product of the magnitudes of the
charges and inversely proportional to the square of the
distance between them.
The equation for this is:
F = kq1q2/r2
F is the magnitude of the force, q1 and q2 are the magnitudes of
the two charges, r is the distance between the charges, and k is
Coulomb's constant with a value of 9.0 x 109 Nm2/C2.
One important thing to remember is that electric forces are
much stronger than gravitational forces involving similar sized
particles.
Example
Find the force on two charges of +0.50 C and +2.0 C if they are
separated by a distance of 3.0 m.
Objects can be charged by conduction or induction. With
charging by conduction, a charged object is brought in contact
with an uncharged object. Electrons flow from negative to
neutral or from neutral to positive to neutralize as much
charge as possible.
With charging by induction, the charged object is brought
near the uncharged object creating regions of positive and
negative charge within the uncharged object.
Objects can also be charged by friction. Electrons may be
transferred from one object to another when they rub together.
An example would be the charge you receive and the spark
that jumps between your hand and a doorknob as you walk on
a carpet. Static generated in a dryer is another example.
Voltage and Electrical Power
Electric potential energy is defined as the work done in
separating charges. Since work must be done to separate
charges, we get energy back if we allow them to get back
together.
Potential difference or voltage is defined as the amount of work
or energy per unit of charge required to move a charge
between two points.
The unit is the volt(v) which is one joule per coulomb(j/c).
If the potential difference is 6v, you get 6 joules of energy out
when 1 coulomb of charge moves between the two points.
The equation for voltage is:
V = W/q
where V is voltage, W is work or energy in joules, and q is the
charge in coulombs.
Example
To separate 0.25 C of charge from another charge, 30 j of work
is done. Find the electric potential energy of the charge. What
is the voltage generated?
A voltage will cause a current to flow between two points on a
conductor. When this happens, there is an opposition to the
current flow called resistance. The unit of resistance is the
ohm(Ω) and is equal to 1 volt per ampere.
Ohm's Law relates voltage, resistance, and current in the
equation:
V = IR
where V is voltage, I is current, and R is resistance.
Example
If a component with a 50 ohm resistance is connected to a 120 v
source, how much current flows through the component?
The parts of a simple electric circuit are shown in the following
diagram. The battery is the source of electric energy, wires
connect the battery to the light bulb, and the light bulb
converts the electric energy to heat and light.
The circuit is said to be open if there is no direct connection at
the switch so that current cannot flow. If the connection is
made so that current can flow, the circuit is said to be closed.
Before electrons were discovered, it was believed that electric
currents consisted of movement of positive charge. Because of
this misconception, conventional current is said to flow from
the positive terminal to the negative terminal. Most devices are
negatively grounded. This does not affect the energy transfer,
only the concept of how it is transferred.
Electric power is defined as work per unit of time just like
mechanical power. The equations, however, are different since
we must write them in terms of voltage, current, and
resistance. The equations are:
P = IV
P = I2R
Example
A car radio draws 0.25 A of current in a 12v system. (a)Find
the power the radio uses. (b)Find the resistance of the radio.
The unit of power is the watt and most electric devices other
than electric motors are rated in watts or kilowatts.
Simple Electric Circuits and Electrical Safety
The two types of electric current are DC and AC. DC stands
for direct current which means the current only flows in one
direction through the circuit. DC is supplied by batteries and
rectifiers.
AC stands for alternating current and means that the current
changes direction in the circuit. In the U.S. this changing
current is called 60 cycle or 60 hz AC since it completes 60
cycles of positive and negative direction each second.
AC is produced by the power companies and is the electric
energy we use in the home to provide energy to most devices.
The two basic ways to connect parts of a circuit are series and
parallel.
In a series circuit, the current flows through one component
after another following just one path. The current is the same
in all parts of the circuit.
Each component uses up some of the voltage so that the total
voltage across the circuit equals the sum of the individual
voltage drops.
To find the total equivalent resistance in the circuit, we simply
add together the magnitudes of all of the individual resistances.
Rs = R1 + R2 + R3
If we were to replace all of the resistances in the circuit with an
equivalent resistance Rs, then the total current in the circuit
would not change.
Example
A student connects a 10 ohm resistor, a 15 ohm resistor, and a
20 ohm resistor in series and connects them to a 50 V DC
voltage source. Find the current in the circuit and find the
power expended in the circuit.
The disadvantage to this type of circuit shows up if one
component fails. Like some Christmas lights, if one bulb burns
out, this opens the circuit so that current cannot flow in any
part of it. In that case they all go out.
Parallel circuit wiring is usually much more convenient. In
parallel wired lights, if one goes out, the rest remain lit.
In a parallel circuit, three light bulbs are wired in parallel. The
current from the battery does not need to go through one of the
bulbs to get to the others. If one were to burn out, each of the
other bulbs would still form a complete circuit and continue to
produce light.
In this circuit, the voltage is the same across each component
since they are all connected to the voltage source at the same
point.
The total current is equal to the sum of the individual currents
and this allows us to derive the formula for the equivalent
resistance in a parallel circuit.
It = I1 + I2 +I3
Vt/Rt = V1/R1 + V2/R2 + V3/R3
since Vt, V1, V2, and V3 are all the same, they divide out
of the equation leaving:
1/Rt = 1/R1 + 1/R2 + 1/R3
Rt is called the equivalent resistance for the circuit. It can
replace the other three resistors without affecting the total
current or power dissipation in the circuit.
The number of resistances in the circuit is not limited to three.
It can vary from 2 up to theoretically an infinitely large
number.
Example
A student connects a 10 ohm resistor, a 15 ohm resistor, and a
20 ohm resistor in parallel and connects them to a 50 v battery.
Find (a) the current in the circuit and (b) the power expended
in the circuit.
When resistances are wired in parallel, the equivalent
resistance is always less than the value of the smallest
magnitude resistor in the circuit.
Household circuits are wire in parallel for two main reasons.
1. The same voltage is available at every connection in the
house. 120 volts is the potential difference between a "hot"
wire and the ground(zero potential wire). Since there are two
incoming potentials, one at +120 v and one at -120 v, air
conditioners, clothes dryers, etc. can be wired across these two
legs to give a potential difference of 240 v.
2. If one appliance is turned off or fails, the others in the circuit
will continue to operate.
Electrical Safety
A fuse can be used to protect a circuit from overload. A fuse is
a device which is wired in series with the circuit it is protecting
and consists of a conductor which will melt when its maximum
current rating is reached. This acts like a switch that opens the
circuit and the current cannot become large enough to damage
the circuit.
Fuses are used in automobiles, audio equipment, and other
devices such as microwave ovens. Fuses may be found in the
household circuits for some older homes. Houses built since
1970 or so will have circuit breakers instead of fuses. A circuit
breaker is an automatic switch which is said to "trip" or open
the circuit when the current gets too high.
Circuit breakers and fuses generally allow a maximum of 20 or
30 amps to flow through an individual circuit.
Another hazard of using electrical devices is the risk of
electrical shock. If a hot wire in a device contacts a metal part
then a person touching this part can receive a shock. This can
be avoided by grounding the case through a third prong on the
connecting wire.
Another type of grounding system uses polarized plugs. One
prong on the plug and one hole in the wall socket are larger
than their counterparts. This is to ensure that you plug the
ground wire prong into the grounded side of the outlet. This
works OK as long as there are no errors made in the wiring of
the socket or the polarized plug.
The three prong plug is safer since the ground wire under
normal conditions carries no current.
Magnetism
A material called lodestone was discovered by the Greeks in a
region of Turkey called Magnesia. Lodestone was used as the
first form of a compass beginning in the twelvth century AD.
Lodestone will align itself with the earth's magnetic field
because there will be two regions on the stone where its
magnetic strength is most concentrated. These regions are
called magnetic poles.
The north pole of a magnet is actually a north seeking pole
since it points north when allowed to freely turn. The same is
true for the south pole of a magnet.
The concept describing the interaction of the poles of two
magnets is called the Law of Poles and it states:
Like poles repel, and unlike poles attract.
The strength of the force depends on the strength of the poles
and is inversely related to the square of the distance between
them.
All magnets are dipoles(they have 2 poles). A magnetic
monopole would consist of a N or S pole without the other. No
magnetic monopole has ever been observed.
A magnetic field is a region of space where a magnetic force is
experienced by a magnet or a ferromagnetic material(iron,
cobalt or nickel). Magnetic fields can be mapped by using a
small compass or iron filings.
Magnetic forces are thought to exist as a result of moving or
spinning charges.
There is always a magnetic field associated with any electric
current. The strength of the magnetic field force depends on
the size of the current. A coil of wire wrapped around an iron
core is called an electromagnet and can be turned on and off as
needed.
Permanent magnets are materials in which electron spin causes
magnetic effects. Most materials are not magnetic because
their electron spin directions are oriented randomly and cancel
each other out. In certain elements(iron, cobalt, nickel), a
significant number of electron spins can be generally aligned.
The areas of alignment are called magnetic domains. If enough
of these domains can be aligned, then the substance becomes a
magnet.
The Earth's Magnetic Field
In the seventeenth century William Gilbert proposed the idea
that the earth acts like a huge bar magnet. The poles of this
imaginary bar magnet are located near the earth's geographic
north and south poles.
The earth's magnetic field exists because of movement of
charged particles within the earth as it rotates.
Since earth's magnetic north does not coincide with the earth's
geographic north, a correction must be made in determining
north with a compass. This correction is called magnetic
declination which is the angle between true north and magnetic
north. Declination changes as you move to the east or west.
Electromagnetism
Electromagnetism is defined as the interaction of electric and
magnetic effects. The two main principles are :
1. Moving electric charges(current) give rise to magnetic fields.
2. Magnetic fields can deflect a moving electric charge.
An example of this interaction occurs in a telephone. The
microphone in a telephone converts sound energy into motion
of a diaphragm and then into an electrical signal that travels
through wires or as radio waves to a receiver which converts
the electrical signal back into sound in a speaker that vibrates
when its magnet interacts with the electric current.
Electric motors convert electrical energy into energy of motion.
An electric current passes through the armature composed of
loops of wire oriented between two magnets called field
magnets. These loops are repelled by both magnets and begin
to turn. At just the right time, the split ring commutator causes
the current to change direction so that the loops are still
repelled by both magnets. As long as electricity is supplied to
the armature, the motor will continue to turn.
This is called a DC motor since it uses batteries or some other
source of DC current. An AC motor works differently and uses
household current.
A generator is a device that converts mechanical energy into
electrical energy. It uses the principle of electromagnetic
induction. Electromagnetic induction occurs when a conductor
and a magnet are in motion relative to each other.
A generator produces either DC or AC voltage depending on
the internal construction of the generator. Most electricity is
generated as AC and is converted to DC with a rectifier as
needed.
One advantage to the use of AC voltage is its ability to be
stepped up to a higher value or stepped down to a lower value.
AC can then be transmitted over great distances at higher
voltage and lower current to avoid energy losses and then
stepped down to the 120 - 240 volts we use in households.
The device that does this is called a transformer and is made of
two separate coils of wire wrapped around a ferromagnetic
metal core. Changes in current in the primary coil(input
voltage) causes a changing magnetic field to exist. This
changing magnetic field induces a current in the secondary
coil(output voltage). The output voltage can be more(stepped
up) or less(stepped down) than the input voltage and depends
on the ratio of the number of turns of wire in the primary
compared to the number of turns in the secondary.
The voltage change for a transformer can be found using the
equation:
V2 = (N2/N1)V1
where V2 is the voltage in the secondary circuit, V1 is the
voltage in the primary circuit, N2 is the number of turns in the
secondary coil, and N1 is the number of turns in the primary
coil.
Example
A transformer has 300 turns in its secondary and 100 turns in
its primary. The primary is connected to a 12 v source.
(a) Is this a step up or step down transformer?
(b) What is the secondary voltage?
(c ) If the transformer is 100% efficient, the power in the
primary equals the power in the secondary. If 2.0 A flows in
the primary, find the current in the secondary.
Study
1. Key Terms, p 186
2. Applying the concepts, p 187 – 189
3. Questions for thought, 3, 5, 6, 9, 11 p 190