Energy in Electrical
Systems
Overview
How can Potential Energy be
stored in electrical systems?
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Battery
•
Stored as chemical energy then transformed to
electrical energy on usage
Water behind a dam
•
Water drives a turbine that generates electrical energy
Capacitor
•
Stores electrical energy as PE
Inductor
•
Stores electrical energy as PE
What is a capacitor?
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An electrical device that separates and
stores electric charge (q)
Characteristics
• Capacitors oppose voltage changes
• Capacitors smooth out voltage changes
How are capacitors made?
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General
•
A capacitor has 2 large
plates of conducting
material separated by an
insulating layer, called the
dialectric.
Shape
•
•
Usually rolled into a
cylinder, or
Variable capacitor (tuners
in radios)
• The more the plates mesh
the higher the capacitance
Examples - Schematic
Work and a Capacitor

Work is done to separate the + and charges on the capacitor plates
• = charging the capacitor
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Work is stored as potential energy in the
capacitor
As the charge increases, the voltage
across the capacitor increases
Units of Capacitance (English &
Metric)

Capacitance is a quantity that reflects the ratio
of net charge stored to the voltage difference
across the plates.
•
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C = q/V
1 Farad (F) = 1 coulomb/1 volt (a very large
value)
Typical values
•
•
Microfarads (x 10-6, F)
Picofarads (x 10-12, pF)
How much energy can be stored
in a capacitor?

Ep = ½ CV2, where

Compare with the amount of energy in a
stretched spring
• Ep = stored electrical potential energy (J)
• C = capacitance (Farads)
• V = voltage (volts)
• Ep = ½ kd2
Capacitance characteristics

Capacitance is determined by
• Area of the plates
• Gap between the plates
• Type of insulating material between the
plates
Example
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
A single-phase 240 V motor has a
capacitor in its starting unit, rated at 50
F (50 x 10-6F).
Find
• The charge stored on the plates
• The potential energy stored in the capacitor
Solution

C = q/V, so

Ep = ½ CV2, so
• q = CV
• q = 50 x 10-6 x 240
• q = 0.012C (coulombs)
• Ep = ½ x 50 x 10-6 x 2402
• Ep = 1.44 J (joule = coulomb/volt)
What is an inductor?

An electrical device used in circuits to oppose changes in
current. (not a resistor that opposes current)
•
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Current change manager
Acts likes a flywheel to smooth out current changes.
•
Called chokes, filters or coils
An Inductor

An inductor builds up voltage in itself to help
overcome the circuit voltage that is causing the
current to change.
•
•
If the circuit voltage increases, the inductor builds a voltage
in the opposite direction.
If the circuit voltage decreases, the inductor adds voltage to
the circuit to help keep the current from increasing.
How are inductors made?
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An inductor is basically a coil of wire, that may or
may not have a core (usually iron)
The inductance of an inductor with an iron core
is much higher than an inductor with an air-core.
Variable inductors allow the core to be moved in
or out of the coil.
Units of Inductance (L)
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An inductor is rated on how much
voltage it can develop to oppose a
certain rate of change in current
Units = Henries (L)
• 1 henry inductor will develop 1 volt whenever
•
•
the current is changing at 1 amp/second
1 henry = 1 volt/(1 amp/sec), or
1 henry = 1 ohm-second
Energy calculations for
inductors?
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The potential energy stored in an
inductor (Ep) is
• Ep = ½ LI2, where
• Ep = energy in joules
• L = inductance in henries
• I = current in amps

Compare with the capacitor
• Ep = ½ CV2
Example
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An inductor has an inductance of 8
henries and a resistance of 2 ohms. The
inductor is connected to a 30V DC
steady power source.
Find
• The energy stored by the inductor
Solution

Find I

Find Ep
• I = V/R (Ohm’s law)
• I = 30/2 = 15 amps
• Ep = ½ LI2
• Ep = ½ x 8 x 152
• Ep = 900 J
How are work and electrical
energy related?
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Capacitor
•
Work is done when voltage charges a capacitor by
moving the charge from one plate to the other. This
work is the Ep.
Inductor
•
Work is done when a voltage pushes a charge through
an inductor – this work is Ep
Electrical work W = charge moved x voltage
difference
•
W=qxV
Workplace applications for caps
and inductors
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Auto ignition
Electronic filter circuits
Helpers for large electric motors