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Electric Circuits
Voltage, Resistance and Power
Voltage
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Volt – Unit of electrical pressure
A VOLTAIC CELL may be described
as a means of converting chemical
energy into electrical energy.
If a load, such as a light, is
connected to the cell, a current will
flow and the light will glow. As the
cell is used, the chemical action
continues until the zinc electrode is
consumed. The chemical equation
for this action would be:
Zn + H2 SO4 + H2OZnSO4 + H20
+ H2
Zinc plus sulfuric acid plus water
chemically reacts to form zinc sulfate
and water and free hydrogen gas.
This cell cannot be recharged
because the zinc has been
consumed. It is called a PRIMARY
CELL. The chemical action cannot
be reversed.
Mercury batteries are rechargeable,
they are called secondary cells.
Batteries use chemicals to make
energy (Chemical Energy) and
generators use movement to make
energy (Mechanical Energy).
Theory of Voltage
Electrical potential energy is useful in solving
problems, particularly those involving charged
particles. But at any point in an electric field,
as the value of the charge increases, the
value of the electrical potential energy
increases.
The electric potential at some point is defined
as the electrical potential energy associated
with a charged particle in an electric field
divided by the charge of the particle.
Although a greater charge will involve a
greater amount of electrical potential energy,
the ratio of that energy to the charge is the
same as it would be if a smaller charge were
at the same position in the field. In other
words, the electric potential at a point is
independent of the charge at that point.
Potential difference is a measure of the
change in the electrical potential energy
divided by the charge. The SI unit for
potential difference (and electric potential)
is the volt, V, and is equivalent to one joule
per coulomb. As a 1 C charge moves
through a potential difference of 1 V,
the charge gains (or loses) 1 J of
energy. The potential difference between
the two terminals of a battery, for instance,
can range from about 1.5 V for a small
battery to about 12 V. The potential
difference between the two slots in a
household electrical outlet is about 120 V.
Remember that only electrical potential
energy is a quantity of energy, with units in
joules. Electric potential and potential
difference are both measures of energy
per unit charge (measured in units of
volts), and potential difference describes a
change in energy per unit charge.
Theory
The value of e has since been
determined to be 1.602 19 x 10-19 C,
where the coulomb (C) is the SI unit of
electric charge. A total charge of —1.0
C contains 6.2 X 1018 electrons (e).
Comparing this with the number of
free electrons in 1 cm3 of copper,
which is on the order of 1023, shows
that 1.0 C is a substantial amount of
charge.
Battery Voltages
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Batteries in Series- In Fig. 2-8,
four cells are connected in
SERIES. The output voltage will
equal,
V =V x n,
V = 1 .5 volts x 4 = 6 volts Out
Notice that the voltage has
increased four times, however, the
capacity of the battery to supply a
current is the same as one cell.
Batteries in Parallel – In Fig. 2-9
the batteries have been connected
together. These cells are
connected in PARALLEL. The total
voltage across the terminals of the
battery is the same as one cell
only. Although the voltage has not
increased, the life of the battery
has been increased because the
current is drawn from all cells
instead of one.
Current
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Current is the rate of charge movement
A current exists whenever there is a net
movement of electric charge through a
medium. To define current more
precisely, suppose positive charges are
moving through a wire. The current is
the rate at which these charges move
through the cross section of the wire. If
ΔQ is the amount of charge that passes
through this area in a time interval, Δt,
then the current, I, is the ratio of the
amount of charge to the time interval.
Current can be direct or alternating
There are two different types of current:
direct current (dc) and alternating
current (ac). In direct current, charges
move in only one direction. In alternating
current, the motion of charges
continuously changes in the forward and
reverse directions. In alternating current,
the terminals of the source of potential
difference are constantly changing sign.
Hence, there is no net motion of the
charge carriers in alternating current;
they simply vibrate back and forth.
Resistance
• RESISTANCE is the
opposition to electric
current in a conducting
wire or material. A large
wire can carry more
electrons than a small
wire. It has less
resistance to the flow,
because of its larger
size.
• Resistance depends on
size and material.
Ohms Law
OHM’S LAW
One of the fundamental laws of electrical circuits was derived from experimentation done by
George Simon Ohm, the German scientist and philosopher, during the 19th century. To honor
the achievements of Mr. Ohm, the standard unit of measurement for resistance is called the
OHM. It is frequently represented by the Greek letter “omega” as . If you see on a diagram
1000 c , it means 1000 ohms. In electronic circuits the use of the kilohm and megohm is very
common. The Greek prefix “kilo” means 1000. The prefix “meg” means one million. These are
summarized in Table 3-2.
Ohm’s Law is stated as: The current in amperes in a circuit is equal to the applied voltage divided
by the resistance, or,
I (in amperes) = E (in volts)/ R (in ohms)
Notice the letter symbols used in this equation:
I = intensity of the current in amperes
E = electromotive force in volts
R = resistance in ohms
In non-mathematical language this formula means:
As voltage is increased
As voltage is decreased
As resistance is increased
As resistance is decreased
— current increases
— current decreases
— current decreases
-— current increases
Using Ohms Law
Series Circuits
• SERIES CIRCUITS
• If a circuit is so arranged that all
of the current flowing in the circuit
will pass through all components,
these components are connected
in SERIES.
• As current passes through a
resistor, a certain amount of
energy is used and a certain
amount of pressure or voltage is
lost. The voltage loss across
each resistor may be calculated
by Ohm’s Law, using formula,
E(V) = I x R,
Series Circuits….
Kirchhoff’s Laws
• Since these resistors are
connected in series, all the
current flowing in the circuit
must pass through each
resistor. Therefore, current is
the same in all parts of the
circuit.
• 1. The sum of the voltage
drops around a series circuit
will equal the source voltage.
• 2. The current is the same
when measured at any point
in the series circuit.
Parallel
Circuits
• When several components are
connected to the same voltage
source, the components are
connected in parallel or “side
by side.” Multiple paths for
current flow are provided by a
parallel circuit, because each
resistor constitutes a path of its
own.
When equal resistors are connected in
parallel, the total resistance of the parallel
network is equal to any one resistor divided
by the number of resistors in the network.
The applied voltage is the same for each
resistor, because each is connected across
the same voltage source.
Therefore, the currents are, using Ohm’s
The total current flowing through the
network would be the sum of the individual
branch currents or:
.2 + .2 + .2 = .6 amps
Parallel Circuits…
Summarizing
• The voltage across all branches of a parallel
network is the same.
• The total current is equal to the sum of the
individual branch currents.
• The total resistance of any parallel circuit must
always be less than the value of’ any resistor in
the network..
• The branch of the circuit containing the greatest
resistance conducts the least current.
Multiple resistors with
different values.
• The conductance of a
circuit is equal to the sum
of the conductances of
the branch circuits.
• Sum the 1/R of the
resistances and then
recipicate the answer.
Parallel Circuits…
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Power
In any electrical circuit, the only component in the circuit
that uses electrical power is resistance. POWER is the
time rate of doing work. In the physics of machines it is
discovered that when a force moves through a distance,
work is done. For example, if a 10 lb. weight is lifted one
foot, the work done equals,
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F (force) x D (distance) or 10 x 1 = l0ft. lb. of work.
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No reference is made to time in this equation. One might
take five seconds or 10 minutes to lift the 10 pound
weight. However, if one lifted the 10 pound weight at the
rate of once each second, then the power expended
would be 10 ft. lb. per second. To carry the example one
step further, if one lifted the 10 pound weight in one-half
or .5 second, then the power expended would equal:
10/5 or 20 ft. lb. per second.
In electricity the unit of power is the watt, named in honor of
James Watt, who is credited with the invention of the
steam engine. When one volt of electrical pressure
moves one coulomb of electricity in one second, the work
accomplished is equal to one watt of power. Recall the
definition of one ampere — when one coulomb of
electrons moves past a given point in a circuit in one
second. So power in an electrical circuit is equal to:
P (watt) = E (volts) x I (amperes)
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Use these figures when comparing electrical power to
mechanical power:
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746 watts = I horsepower
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The power formula, sometimes called Watt’s law, can be
arranged algebraically, so that if two quantities are
known, the third unknown may be found.
Example: A circuit with an
unknown load has an applied
voltage of 100 volts. The
measured current is 2 amperes.
How much power is consumed?
P = I x E or 2amps x I00V = 200W
Example: An electric toaster
rated at 550 watts is connected
to a 11 0 volt source. How
much current will this
appliance use?
Power and Circuits
• POWER IN A SERIES CIRCUIT
• As the voltage overcomes the
resistance, work is done and power
is the time rate of doing work.
Referring to the section on power,
earlier in this chapter, you will
discover that in electricity, P = I x E.
The energy lost in overcoming the
resistance takes the form of heat.
This must be dissipated by the
resistor into the surrounding air. This
explains why some resistors are
larger than others. They must be
large enough to provide radiation
surface for heat dissipation.
Formulas
If you have two of the four
variables you can solve for
the others.