Download 2. Power and Resistors

WORK, ENERGY AND POWER
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Work – energy spent to overcome a restraint to achieve
a physical change
Energy is the ability to do work
Energy and work have the same SI units – Joules (J)
Power – rate at which energy is expended (Joules/sec)
Unit of power = watt = Joules per second = Js-1
Power (P) = Work (W)/Time (t); W = Pt
When electrical current flows through a resistance,
electrical energy is converted to heat energy at a rate
that depends on the voltage across the resistance and
the value of current through it, i.e.
Power (P) = Voltage (V) × Current (I) (watts)
P = V2/R = I2R (watts)
Power ‘delivered’ to a resistance = power dissipated in
resistance
A kilowatt-hour (kWh) is the total energy delivered or
consumed in one hour, and is used in industry
kWh = (P in kW) × (t in hours)
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WORK, ENERGY AND POWER
EXAMPLES
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A 12V DC power source is connected to a 500Ω
resistor that has a tolerance of ±5%. What is the
maximum and minimum power that can be dissipated in
the resistance?
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Electrical energy costs £0.12/kWh. For how long could
a 900W oven be operated without costing more than
36p?
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POWER RATING OF RESISTORS
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If the power rating of a resistor is too small for a
particular application, then the resistor will not be able
to dissipate heat at a rate rapid enough to prevent
destructive temperature build up
Resistors that are physically large in size have a
greater surface area, so they dissipate heat faster
Resistors are used to control the flow of current in part
of a circuit
Question: A 200Ω resistor has a 2W power rating.
What is the maximum current that can flow in the
resistor without exceeding the power rating?
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TEMPERATURE CHARACTERISTICS
OF RESISTORS
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Resistors are constructed from metal alloys (hybrids of
more than one element), metal oxide (metals containing
oxygen atoms) films or carbon composites.
Resistance values of resistors are dependent on
temperature.
Rθ = R0 (1 + aθ )
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Rθ is the resistance at temperature θ
R0 is the resistance at 0°C
a is the temperature coefficient
θ is the temperature in °C
Example What is the value of a 6.8kΩ resistor at 95°C
if the temperature coefficient is 1.2e-3?
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Example If a resistor with a temperature coefficient of
1.5e-3 has a value of 10Ω at 20°C, what is its
resistance at 80°C?
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RESISTOR COLOUR CODES
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0
1
2
3
4
5
6
7
8
9
5%
10%
20%
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Yellow; violet; orange;
silver = 47×103Ω ±10%
Brown,black,red?
Blue,grey,black,gold?
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Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Grey
White
Gold
Silver
None
1st
2nd
3rd
Tolerance
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STANDARD RESISTOR VALUES
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Resistors are available in a number of standard ranges
These ranges, or series, are set up by the Electronics
Industries Association (EIA)
They are: E3, E6, E12, E24, E48, E96, E192
The number after the ‘E’ denotes the number of values
the series contains per decade (every factor of 10)
Resistors with a tighter tolerance can have more values
in the series that won't overlap one another
E3: 50% tolerance
E6: 20% tolerance
E12: 10% tolerance
E24: 5% tolerance
E48: 2% tolerance
E96: 1% tolerance
E192: less than 1% tolerance
http://www.hardwarebook.info/EIA_resistors
Question: A 9V battery is connected to an E12 resistor
of 560Ω. What is the range of possible current flow in
such a circuit?
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STANDARD PREFIXES AND
SYMBOLS
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Pico (p) ×10-12 e.g. 1.8p
Nano (n) ×10-9 e.g. 4.7n
Micro (µ) ×10-6 e.g. 0.1µ
Milli (m) ×10-3 e.g. 10m
Kilo (k) ×103 e.g. 9.8k
Mega (M) ×106 e.g. 1M
Giga (G) ×109 e.g. 1.8G
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CONDUCTANCE
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Conductance is the reciprocal of resistance
Conductance is the ability of a material to pass
electrons
The higher the resistance, the lower the conductance
Symbol of Conductance is G
Unit of conductance is the Siemen (S)
G = 1/R Siemens
What are the resistance and conductance ranges of a
75kΩ ± 10% resistor?
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