Transcript Ohms Law, Energy and Power

Ohm’s Law, Energy & Power
MECH1100
Chapter 3 – Ohms Law, Energy and Power
Topics
Ohm’s Law
Energy and Power
Power Ratings
Energy Conversion and Voltage Drop
Power Supplies and Batteries
Troubleshooting
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Review of V, I, and R
Voltage is the amount of energy per charge available to
move electrons from one point to another in a circuit
and is measured in volts.
Current is the rate of charge flow and is measured in
amperes (amps).
Resistance is the opposition to current and is measured
in ohms.
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Ohm’s law
• Most important fundamental law in electronics
• Relates voltage, current, and resistance.
• Georg Simom formulated the equation
V
I
R
I = Current
V = Voltage or energy (E)
R = Resistance
What is the current in a circuit with a 12 V source if
the resistance is 10 W? 1.2 A
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If you need to solve for voltage,
Ohm’s law is: V  IR
What is the voltage across a 680 W resistor if the
current is 26.5 mA? 18 V
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If you need to solve for resistance,
Ohm’s law is:
V
R
What is the resistance of
the bulb? 132 W
I
OFF
V
Hz
115 V
V
mV
A
Range
Autorange
Touc h/Hold
1s
1s
10 A
V
40 mA
COM
Fused
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IF:
1. Resistance is held Constant and
2. Voltage Changes
3. What happens to current?
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V
I
R
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IF:
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1. Resistance Changes and
2. Voltage is held Constant
3. What happens to current?
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What is the System Current?
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1
G= R
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A student takes data for a resistor and fits the
straight line shown to the data. What is the
conductance and the resistance of the resistor?
16
14
14.8 mA - 0 mA
G
 1.48 mS
10.0 V - 0 V
The reciprocal of the
conductance is the
resistance:
1
1
R 

 676 Ω
G 1.48 mS
I (mA)
The slope represents the
conductance.
12
8
4
0
0
2
4
6
8
10
V (V)
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Graphic aid for the Ohm’s law
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What is the system current
State your knowns and value required!!
100
V
I
R
5.0
100
I=
I = 20*10-3 amp or “X?” mAmp
3
5 * 10
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What is the System Voltage?
56k
Vs = IR Vs = 5 x 10-3 amp * 56 x 103 ohms Vs = 280 volts
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What is the Resistance of the
Photocell?
9.0
Vs
R
Is
R = 5696.2 ohms (5.69 kΩ)
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Energy and Power
When a constant force is applied to move an object over
a distance, the WORK (W) is the force times the
distance.
The force must be measured in the same direction as
the distance. The unit for work is the newton-meter
(N-m) or joule (J).
Distance
Force
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One joule is the work done when a force of
one newton is applied through a distance of
one meter. A joule is a small amount of work
approximately equal to the work done in
raising an apple over a distance of 1 m.
The symbol for energy, W, represents
work, but should not be confused with the
unit for power, the watt, W.
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1n
1m
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• Energy is closely related to work.
• Energy is the ability to do work.
1. Measured in the same units as work,
2. Newton-meter (N-m) (same as a joule (J)).
What amount of energy is converted to heat in
sliding a box along a floor for 5 meters if the
force to move it is 400 n?
W = Fd = (400 N)(5 m) = 2000 N-m = 2000 J
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Energy and Power
Power is the rate of doing work.
• Rate means a time unit is required.
• Joule per second (J/s) = one watt (W).
Work
W
(energy in
P
joules) not
t
Watts
What power is developed if the box in the previous
example is moved in 10 s?
P
W 2000 J

 200 Watts
t
10 s
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Electrical Energy to Thermal Energy
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A loss of energy (voltage) by electrons (charge) as
they flow through a resistance
1. creates a voltage drop
2. because voltage equals energy divided by charge.
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The kilowatt-hour (kWh) is a much larger unit of
energy than the joule.
• 3.6 x 106 J in a kWh.
• kWh is convenient for electrical appliances.
What is the energy used in operating a
1200 W heater for 20 minutes?
1200 W = 1.2
? kW
1.2 kW X 20minutes/60 minutes/hr = 0.396 kWh
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In electrical work, the rate energy is dissipated is
dependent on the amount of resistance and the
amount of current.
Thus: P = I*V
and
V = I*R
Therefore: P  I 2 R
or
V2
P
R
Together, the three forms are called Watt’s law.
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What power is dissipated in a 27 W resistor if the
current is 0.135 A?
Given that you know the resistance and current,
substitute the values into P =I 2R.
P  I 2R
 (0.135 A) 2  27 W 
 0.49 W
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What power is dissipated by a heater that draws 12 A
of current from a 120 V supply?
The most direct solution is to use P = IV.
P  IV
 12 A 120 V 
 1440 W
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What power is dissipated in a 100 W resistor with 5 V
across it?
The most direct solution is to use
V2
P
R
V2
P
R
5 V


 0.25 W
100 W
2
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Power rating of a resistor
Amount of power a resistor can dissipate without being
damaged by the heat generated
Small resistors operating in low
voltage systems need to be sized
for the anticipated power.
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Resistor failures
• Resistor failures are unusual except when they have
been subjected to excessive heat.
• Look for discoloration (sometimes the color bands
appear burned).
• Test with an ohmmeter by disconnecting one end
from the circuit to isolate it and verify the resistance.
• Correct the cause of the heating problem (larger
wattage resistor?, wrong value?).
Normal
Overheated
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Metal film resistors come in standard
power ratings: 1/8 to 1 watt
Always choose a resistor
with a higher power
rating than the power
being used in the circuit
so that the resistor isn't
destroyed by excess
heat!
1
W
8
1
W
4
1
W
2
1W
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Choosing the correct resistor
What power rated resistor would you chose for
each circuit?
0.833 W => 1 Watt
0.100 W => .125 Watt
A resistor on a control board is calculated to require a
power of 0.25W. What power rated resistor would
you choose?
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Troubleshooting
Some questions to ask before starting any
troubleshooting are:
1. Has the circuit ever worked?
?
2. If the circuit once worked, under what
conditions did it fail?
3. What are the symptoms of the failure?
4. What are the possible causes of the failure?
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Troubleshooting
• Plan the troubleshooting by reviewing
pertinent information:
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?
1. Schematics
2. Line drawings
3. Ladder logic
4. Instruction manuals
•
Then review when and how the failure occurred
•
Always, talk with the operator or anyone else having
knowledge of the failure
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• OPEN or open circuit
An electric circuit in which the
normal path of current has been
interrupted, either by the
disconnection of one part of its
conducting pathway from another,
or by the intervention of an electric
component, such as a transistor.
SHORT or Short Circuit
A faulty or accidental connection between two points
of different potential in an electric circuit, bypassing
the load and establishing a path of low resistance
through which an excessive current can flow.
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Half-splitting method of
troubleshooting
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Power Wheel
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Key Terms
Ohm’s law A law stating that current is directly
proportional to voltage and inversely
proportional to resistance.
Linear Characterized by a straight-line relationship.
Energy The ability to do work. The unit is the joule (J).
Power The rate of energy usage.
Joule The SI unit of energy.
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Key Terms
Watt The unit of power. One watt is the power
when 1 J of energy is used in 1 s.
Kilowatt-hour A common unit of energy used mainly by
utility companies.
Ampere-hour A number determined by multiplying the
rating current (A) times the length of time (h) that a
battery can deliver that current to a load.
Efficiency The ratio of output power to input power of a
circuit, usually expressed as a percent.
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1. When the current is plotted against the voltage for a
fixed resistor, the plot is a
a. straight line with a positive slope
b. straight line with a negative slope
c. parabola
d. hyperbola
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2. For constant voltage in a circuit, doubling the resistance
means
a. doubling the current
b. halving the current
c. there is no change in the current
d. depends on the amount of voltage
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4. If the current in a 330 W resistor is 15 mA, the voltage
across it is approximately
a. 5.0 V
b. 22 V
c. 46 V
d. 60 V
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5. A unit of power is the
a. joule
b. kilowatt-hour
c. both of the above
d. none of the above
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6. The SI unit of energy is the
a. volt
b. watt
c. joule
d. kilowatt-hour
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7. If the voltage in a resistive circuit is doubled, the power
will be
a. halved
b. unchanged
c. doubled
d. quadrupled
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8. The approximate power dissipated by a 330 W resistor
with 9 V across it is
a. ¼ W
b. ½ W
c. 1 W
d. 2 W
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9. Before troubleshooting a faulty circuit, you should find
out:
a. If the circuit ever worked
b. The conditions that existed when it failed
c. The symptoms of the failure
d. All of the above
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