Applied Circuit Analysis
Chapter 3 Power and Energy
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Power and Energy
• Energy (E) is the ability to do work
• Power (P) is the rate of expending
energy
• They are related as follows:
P
W
t
• Where t is time in seconds
• Power is measured in Watts (W) while
energy is measured in Joules (J)
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Other Units
• Another familiar unit of measurement for
power is the horsepower (hp)
• This unit was introduced by James Watt
• One hp is equal to approximately 0.75kW
• Electric companies, commonly measure
energy with power x time
• The unit used is typically the watt-hour (Wh)
kilowatt-hour (kWh)
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Power in Electric Circuits
• In a circuit, power is defined by the
product of current and voltage:
P  VI
• If we incorporate Ohm’s law (V=IR), we
can express power in terms of other
circuit quantities:
2
V
P  I 2R P 
R
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V, I, R, and Power
• The four parameters, V, I, R, and P can
be related to each other as shown:
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Power Sign Convention
• Current direction and
voltage polarity determine
the sign of the power in a
circuit element.
• In passive sign convention,
power is positive when
current enters the positive
terminal of the element.
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Passive Sign Convention
• In this convention, positive
power represents the
situation where the
element in question is
absorbing energy.
• When the power is
negative (like shown), the
element is supplying
power.
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Resistor Power Ratings
• In addition to the value of resistance, a
resistor usually has a rating for its
power specified.
• This rating is the maximum power it
can handle without it becoming too hot
or risking damage to it.
• The power rating is dependent on its
physical size; the larger the size, the
more power it can handle.
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Resistor Power Ratings II
• The common carbon or metal film
resistors come in ratings ranging from
1/8th W to 2 W.
• The most commonly found are either
the 1/8th or the ¼ W.
• Resistors with power rating above 2W
are wirewound.
• These can range from 5W to 200W
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Efficiency
• The efficiency of a device
is a means of comparing
its useful output to the
input required to run it.
• In a device, some of the
input power will be “lost”
in a form that is unusable.
• This is typically in the
form of heat.
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Efficiency II
• Efficiency (η) can be expressed in
terms of power:
Pout

 100%
Pin
• Or in terms of energy
Wout

 100%
Win
• In both cases it may never exceed
100%
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Fuses
• As we know, power dissipated in
resistors varies as the square of the
current.
• Wiring in buildings, though very
conductive, is not without some
resistance.
• If excess current passes through the
wires, they will heat up and potentially
ignite surrounding materials.
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Fuses II
• To prevent this from happening,
protective devices are required, which
will interrupt the flow of current.
• The most basic protective device is the
fuse.
• Fuses are single use devices that
create an open circuit when current
exceeds their rated value.
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Fuses III
• A fuse consists of a thin metal wire
enclosed in a cartridge, which is
inserted into a receptacle built within
the circuit.
• In its pristine state, the fuse has very
low resistivity (it may read 0 Ohms on
an ohmmeter).
• In this state, it conducts current to the
circuit as would a wire.
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Blown Fuse
• Each fuse has a specifically
designed thickness of wire that
will heat up as the current
through it increases.
• At the rated value, the wire will
melt, and result in a broken
connection, thus halting the
flow of current.
• This is referred to as a “blown
fuse”
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Causes of blown fuses
• One of the most common causes for a
blown fuse is the sudden development
of a short circuit.
– This may be due to the introduction of a
conducting object (screwdriver across
terminals)
– It may also be due to failure of a
component, such as a capacitor.
• Another cause is too many loads
drawing too much current.
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Circuit Breaker
• Fuses for the most part continue to be
used in electronic appliances.
• In households, however, it is far more
common now for a more advanced
protective device to be used: The
circuit breaker.
• The function remains the same, current
exceeding the rated value causes an
open circuit.
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Circuit Breaker II
• The key difference is that unlike a fuse,
the circuit breaker can be reset.
• It works by using a spring that expands
with heat.
• When heated beyond a specified point,
a switch is activated that opens the
circuit.
• The breaker can then be manually
reset.
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Ground Fault
• Fuses and circuit breakers are designed to
protect buildings and equipment from
damage due to too much current.
• They are not effective in protecting people
from receiving shocks however.
• There does exist a protective device that
serves that role.
• It is called the ground fault circuit interrupter
(GFCI)
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Ground Fault II
• The concept of grounding was
developed to protect against electric
shock.
• But in certain situations current can
flow along the ground path.
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Ground Fault III
• The situation that comes to mind most
readily is an appliance falling into a
bathtub.
• If a person becomes part of the return
path injury or death can occur.
• Recall that only a few tens of mA are
required for injury.
• This is not enough to trigger a fuse or
circuit breaker.
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GFCI
• The GFCI operates by sensing the
current leakage.
• The current along the hot wire and
neutral wire are compared.
• If any difference is sensed then current
may be passing through the ground
path.
• If so, the GFCI breaks the circuit just
like a circuit breaker.
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GFCI II
• They can either be in
wall outlets or
installed at the circuit
breaker to protect an
entire building.
• A typical wall outlet
version is shown
here.
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Wattmeter
• Power consumption in a AC system
can be measured using a
Wattmeter.
• The meter consists of two coils; the
current and voltage coils.
• The current coil is designed with
low impedance and is connected in
series with the load.
• The voltage coil is designed with
very large impedance and is
connected in parallel with the load.
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Wattmeter II
• The induced magnetic field from both
causes a deflection in the current coil.
• Ideally, the configuration does not alter
the load and affect the power
measured.
• The physical inertia of the moving coil
results in the output being equal to the
average power.
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Watt-hour meter
• The watt-hour
meter shown
should be familiar
to everyone.
• It will measure
accumulated
kilowatt-hours.
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Watt-hour meter
• The meter works by using a motor who
torque is proportional to the current
flowing through it.
• The motor turns a register that counts
the number of revolutions the motor
makes.
• This, though a series of gears moves
dials indicating the energy used.
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