Download ENERCY AND POWER

r INTRODUCTION
AND
ENERCY
POWER
4-1
F2
4:3
H
q-5
4-6
Energyand Power
Powerin an ElectricCircuit
ResistorPowerRatings
EnergyConversionand Voltage
Drop in Resistance
PowerSupplies
TechnologyTheoryinto Practice
(EWB)
and
Workbench
Electronics
PSpiceTutorialsavailableat
prenhall.com/floYd
http://www.
From Chapter 3, you know the relationship of current,
voltage, and resistanceas statedby Ohm's law. The
existenceof these three quantities in an electric circuit
results in the fourth basic quantity known as power. A
specific relationship exists between power and I, V
and R, as you will leam.
Energy is the ability to do work, and power is
the rate at which energy is used. Current carries electrical energy through a circuit. As the free electrons
pass through the resistanceof the circuit, they give up
their energy when they collide with atoms in the resistive material. The electrical energy given up by the
electrons is converted into heat energy' The rate at
which the electrical energy is used is the power in the
circuit.
In the TECH TIP, Section 4-6, you will see how
the theory learned in this chapter is applicable to the
resistancebox introduced in the last chapter. Suppose
your supervisor tells you that the resistancebox is to
be used in testing a circuit in which there will be a
maximum of 4 V across all the resistors.You are
askedto evaluatethe power rating of each resistor
and, if it is not sufficient, to replace the resistor with
one that has an adequatepower rating.
r TECHnology
Theory
Into
Practice
r CHAPTER
OBfECTIVES
tr Delineenergy andpower
E Calculap
t eo w e ri n a c i r c u i t
J Properlyselectresistorsbasedon power
consideration
B Explain energyconversionand voltagedrop
Discusspower suppliesand their characteristics
FggSgdBKtsHOAW,ru€FKW]S
James Prescott Joule
I818-1889
JamesPrescottJoule was a British
physicist who was born in Salfbrd,
Lancashire,in 1818.Joule is known
for his research in electricity and thermodynamics. He
formulatedthe relationship that statesthat the amount of
heatenergyproduced by an electric current in a conductor is related to the conductor's resistance and the time
(energy= power x time). The unit of energy is named in
his honor.Photo credit: Library of Congress.
James Watt
1 7 3 61 8 1 9
James Watt was a Scottish inventer
and mechanical engineer who was
born in Greenock in 1736. He is
renowned for his improvements to the steam engine
which made it practical for industrial use. Watt designed
a separatecondensing chamber that prevented enormous
loss of steam in the cylinder and enhanced the vacuulr
conditions. Watt's {irst patent was on this device, but he
also patented several other inventions, including the
rotary engine. The unit of power is named in his honor.
Photo credit: Lihrarl of Congress.
92 I
AND POWER
ENERCY
4_1 I ENERCY
AND POWER
When there is cutent throagh a resistance, electricql energy is converted to heat or
other form of energy, such qs light. A common example of this is a light bulb that
becomestoo hot to touch. The cunent throagh the filament that produces light also
produces unwanted heat becausethe filament has resistunce, Power is a measare of
how fast energy is heing used; electrical components must be uble to dissipate a certain amount of energy in a given period of time,
After completing this section, you should be able to
I Define energy and power
. Express power in terms of energy
. State the unit of power
. State the common units of energy
. Perform energy and power calculations
By definition,
Energy is the ability to do work; and power is the rate at which energy is
used.
In other words, power, symbolized by 4 is a certain amount of energy used in a certain
length of time, expressedas follows:
energy
rower = --l:
tlme
w
P = -:-t
(4-1)
Energy is measured in joules (J), time is measured in seconds (s), and power is
measuredin watts (W). Note that an italic lV is used to representenergy in the form of
work and a nonitalic W is used for watts, the unit of power.
Energy in joules divided by time in secondsgives power in watts. For example, if
50 J of energy are used in 2 s, the power is 50 J/2 s = 25 W. By definition,
One watt is the amount of power when one joule of energy is used in one
second.
Thus, the number of joules used in one second is always equal to the number of watts.
For example, if 15 J are used in I s, the power is 75 W.
EXAMPTE 4-1
An amountof energyequal to 100 J is used in 5 s. What is the power in watts?
so l u ti o n
p=9Ts
tlme
- w - 4U= 2ow
/
)s
RelatedProblem If 100W of poweroccursfor 30 s, how muchenergy,in joules,is
used?
Amounts of power much less than one watt are common in certain areas of electronics. As with small current and voltage values, metric prefixes are used to designate
small amounts of power. Thus, milliwatts (mW), microwatts (pW), and even picowatts
(pW) are commonly found in some applications.
ENERCY
AND POWER T 93
In the electrical utilities fleld, kilowatts (kW) and megawatts (MW) are common units. Radio and television stations also use large amounts of power to transmit
signals.
EXAMPLE4 -2
Expressthe following valuesof electricalpowerusingappropriatemetricprefixes:
(a) 0.045w
(b) 0.000012w
(c) 3500W
(d) 10,000,000
w
Solution
(a) 0.045W = 45 mW
(c) 3500W = 3.5 kW
(b) 0.000012
W = 12 pW
(d) 10,000,000
W = 10 MW
RelatedProblem Expressthe following amountsof powerin wattswithout metric
prefixes:
(b) 1800pW
(c) 1000mW
(a) 1 mW
(d) 1 p.W
The Kilowatt-hour(kwh) Unit of Energy
Since power is the rate at which energy is used, as expressedin Equation (4-l), power
utilized over a period of time representsenergy consumption. If you multiply power and
time, you have energy, W
Energy=powerxtime
W=Pt
(4 -2)
Previously, the joule was defined as a unit of energy. However, there is another
way to expressenergy. Since power is expressedin watts and time in seconds,units of
energy called the watt-second (Ws), watthour (Wh), and kilowatt-hour (kWh) can be
used.
When you pay your electric bill, you are charged on the basis of the amount of
energy you use, not the power. Becausepower companiesdeal in huge amounts of energy,
the most practical unit is the kilowatt-hour. You use a kilowatt-hour of energy when you
use one thousand watts of power for one hour. For example, a 100 W light bulb burning
for 10 h uses I kWh of enersv.
w = Pt = (100w)(10 h) = 1000wh = I kwh
EXAMPTE4-3
Determinethe numberof kilowatt-hours(kWh) for eachof the following energyconsumptions:
(a) 1400Wforlh
(b) 2500Wfor2h
(c) l00,000Wfor5h
Solution
(a) 1a00W = 1.4kW
w = p t = ( l . 4 k w ) ( 1h ) = 1 . 4 k w h
(c) 100,000
W = 100kW
w= (100kwxs h) = 500 kwh
(b) 2500W = 2.5kW
w = ( 2 . 5k w x 2 h ) = 5 k w h
Related Problem How many kilowatt-hoursare used by a 250 W bulb burning
for 8 h?
94 T
ENERCYAND POWER
SECTION 4-1
REVIEW
1. Definepower
andtime.
2. Writetheformulafor powerin termsof energy
3. Definewatt.
4. Express each of the following values of power in the most appropriate units:
(c) 0.000025w
(b) 0.005W
(a) 68,000W
of powerfor 10 h, how muchenergy(in kWh) haveyou used?
5. If you
"t: i99-*
6. Convert2000Wh to kilowatt-hours.
7. Convert360,000Ws to kilowatt-hours.
CIRCUIT
4_2 . POWERIN AN ELECTRIC
The generatian of heat, which occurs when electrical energy is converted to heat
energy, in an electric circuit is often an unwunted,by-product of current through the
resistance in the circuit. In some cases,however, the generation of heat is the primary
parpose of a circuit as, for example, in an electric resistive heuter. In any case, yoa
must always deal with power in electrical and electronic circuits.
After completing this section, you should be able to
I
Calculate power in a circuit
. Determine power knowing l and R
. Determine power knowing V and 1
. Determine power knowing V and R
When there is current through resistance,the collisions of the electrons produce heat, as
a result of the conversionof electrical energy,as indicated in Figure 4-1. There is always
a certain amount of power in an electric circuit, and it is dependent on the amount of
resistanceand on the amount of current, expressedas follows:
P=I2R
(4-3)
We can get an equivalent expressionfor power by substituting V fot IR (f is 1 x L;.
P = I'R = (1x 1)R = (1R) = (1RX
P = Vl
@-4)
g V/R for 1 (Ohm'slaw) asfollows:
by substitutin
Weobtainanotherequivalentexpression
P=VI=
v(v\
\R/
p=t
(4-5)
R
FIGURE 4_1
Power in an electric circuit results
heat energy given off by the
resistance.
Heat produced by
current through
resistanceis a result
of energy conversion,
POWERlN AN ELECTRIC
CIRCUIT I
95
The relationships expressedin the preceding formulas are known as Watt's law. In each
case,l must be in amps, V in volts, and R in ohms.
Usingthe AppropriatePowerFormula
To calculate the power in a resistance,you can use any one of the three power formulas,
depending on what information you have. For example, assumethat you know the values
of current and voltage. In this case you calculate the power with the formula P = VI. If
you know 1 and & use the formula P = Pn. If you know V and R, use the formula
P = V"/R.
EXAMPLE
4-4
Calculate the power in each of the three circuits of Figure 4-2.
4'I Q
100
F I C U R E4 - 2
Solution
In circuit (a), V and 1 are known. Therefore, use Equation (4-4).
P=VI=(10VX2A)=20W
In circuit (b), l and R are known. Therefore, use Equation (4-3).
P = I2R = (2 A)2(47 O) = lgg W
In circuit (c), V and R are known. Therefore, use Equation (4-5).
p = L = ( 5 , v ]=' 2 . s w
R
lOO
Related Problem Determine P in each circuit of Figure 4-2 for the following
changes:
Circuit (a): l doubled and Vremains the same
Circuit (b): R doubled and l remains the same
Circuit (c): V halved and R remains the same
EXAMPLE
4-5
A 100 W light bulb operateson 120 V. How much current does it require?
Solution Use the formula P = VI and solve for l by first transposingthe terms to get
1 on the left of the equation.
VI=P
Divide both sides of the equation by V to get 1 by itself.
W
Y
P
V
96 T
ENERCY
AND POWER
The lzs cancel on the left, leaving
t=L
v
100W for P and 120 V for Vyields
199* =
'I - L =
0.833
A = E33mA
v
l20v
RelatedProhlem A lisht bulbdraws545mA from a 11[
power?
SECTION4-2
REVIEW
source. What is the
1. Ifthere are 10 V acrossa resistorand a currentof 3 A throughit. what is the power?
2. How much power doesthe sourcein Figure 4-3 generate?What is the power in the
resistor?Are the two valuesthe same?Why?
FICURE4-3
3. If there is a current of 5 A through a 56 Q resistor,what is the power?
4. How much power is dissipatedby 20 mA through a 4.7 kQ resistor?
5. Five volts are appliedto a l0 O resistor.What is the power?
6. How much power doesa 2.2 kCl resistorwith 8 V acrossit dissipate?
7. What is the resistanceof a 75 W bulb that takes0.5 A?
4_3 . RESISTOR
POWERRATINCS
As you already know, a resistor gives off heat when there is current through it. The
limit to the amount of heat thut a resistor can give off is specified by its power rating.
After completing this section, you should be able to
I Properly select resistors based on power consideration
. Define power rating
. Explain how physical characteristicsof resistors determine their power rating
. Check for resistor failure with an ohmmeter
The power rating is the maximum amount of power that a resistor can dissipate without being damaged by excessive heat buildup. The power rating is not related to the
ohmic value (resistance)but rather is determined mainly by the physical composition,
size, and shapeof the resistor.All else being equal, the larger the surface area of a resistor, the more power it can dissipate.Ignoring the area of the ends, the surface area of a
cylindrically shaped resistor is equal to the length (l) times the circumference (c), as
indicated in Figure 4-4.
RESISTOR
POWERRATINGS .
97
Mn
Ccircumrerence(c)
Surfacearea=/xc
F I G U R E4 . 4
The power rating of a resistor is directly related to its surfoce area,
Metal-film resistors are available in standardpower ratings from % W to I W as
shown in Figure 4-5. Available power ratings for other types of resistors vary. For example, wirewound resistors have ratings up to 225 W or greater. Figure 4-6 shows some
of theseresistors.
FlcuRE 4-5
Relativesizesof metal-filmresistorswith standardpower
ratings of 1/a,w, I/d w, 1/zw, and I w.
**"***********.".."".""""
."*_**
" "" ^ fi,o,,.l]__**_**
y'"\rr"-|-r
--lllt-
(a) Axial-lead wire wound
(b) Adjustable wire wound
(c) Radial-lead for PC board insertion
4-6
FIGURE
Ijpical resistorswith high power ratings.
Selectingthe ProperPowerRatingfor an Application
When a resistor is used in a circuit, its power rating must be greater than the maximum
power that it will have to handle. For example, if a resistor is to dissipate 0.75 W in a
circuit application, its rating should be at least the next higher standard value which is
I W. Ideally, a rating that is approximately twice the actual power should be used when
possible.
98 I
ENERCYAND POWER
ratingfor eachof themetal-nlm
resistors
in Figure4-7
EXAMPLE
4-6
3l\tr,";V1;qr:ht"ilrT
r0v
(a)
(b)
FIGURE4-7
Solution
In Figure 4--7(a), the actual power is
("9^?'=
=0.833w
P=4=
lqqY
R
l20o
120c)
Select a resistor with a power rating higher than the actual power. In this case, a 1 W
resistor should be used.
In Figure 4-:7(b), the actual power is
p = IzR = (10 mA)2(1000o) = (10 x t0-3 A)2(1000e) = 9.11ry
At least a%W (0.125W) resistorshouldbe used in this case.
Related Problem A certain resistor is required to dissipate 0.25 W. What standard
ratins should be used?
ResistorFailures
When the power in a resistor is greaterthan its rating, the resistor will become excessively
hot. As a result, either the resistor will burn open or its resistancevalue will be greatly
altered.
A resistor that has been damagedbecauseof overheating can often be detected by
the charred or altered appearanceof its surface. If there is no visual evidence, a resistor
that is suspectedof being damaged can be checked with an ohmmeter for an open or
incorrect resistancevalue. Recall that one or both leads of a resistor should be removed
from a circuit to measureresistance.
Checkinga Resistor
with an Ohmmeter
A typical analog multimeter (VOM) and a digital multimeter are shown in Figures 4-8(a)
and a-8@), respectively.The large switch on the analog meter is called a range switch.
Notice the resistance(OHMS) settings on both meters. For the analog meter in part (a),
each setting indicates the amount by which the ohms scale (top scale) on the meter is to
be multiplied. For example, if the pointer is at 50 on the ohms scale and the range switch
is set at x10, the resistancebeing measuredis 50 x 10 O = 500 fl. Ifthe resistor is open,
the pointer will stay at full left scale (* means infinite) regardlessof the range switch setting.
For the digital meter in Figure 4-8(b), you use the range switch to select the
appropriate setting for the value of resistancebeing measured.You do not have to multiply to get the correct reading because you have a direct digital readout of the resistance value.
RESISTOR
POWERRATINCS T 99
(4,
FIGURE4-B
Typi.calportable muhimeters (photographycourtesy of B&K Precisinn (Corp.).
EXAMPLE
4-7
Determine whether the resistor in each circuit of Figure 4-9 has possibly been damaged by overheating.
V2W
1.5ko
-l
I
24V
I
Solution In the circuit in Figure4-9(a),
F' =
v2 = f(9
f iv\2
-=0.810W=8l0mW
^
The rating of the resistor is 7+W (0.25 W), which is insufficient to handle the power.
The resistor has been overheatedand may be burned out, making it an open.
In the circuit of Figure 4-9(b),
P
= v 2 = fQf i4-V=\ 20 . 3 8 4 W = 3 8 4 m W
R
The rating of the resistor is VzW (0.5 W), which is sufficient to handle the power.
In the circuit of Figure 4-9(c),
p =t-
R
(5v)'z
= 2.5w
1OO
t l
t l
llrl
1OOT
ENERCY
AND POWER
The ratingof the resistoris I W, which is insufficient to handle the power. The resistor hasbeenoverheated
andmay be burned out, making it an open.
RelatedProblem A 0.25 W
the powerrating adequate?
SECTION
REVIEW
4-3
resistoris connectedacrossa 12 V battery.Is
1. Name two important values associatedwith a resistor.
2. How does the physical size of a resistor determine the amount of power that it can
handle?
3. List the standardpower raringsof metal-film resistors.
4. A resistor must handle 0.3 W. What minimum power rating of a metal-film resistor
should be used to dissipatethe energyproperlyl
4-4 S ENERCYCONVERSION
AND VOTTAGE
DROP IN RESISTANCE
As you have seen, when there is current through a resistance, electrical energy is
converted to hest energy. This heut is caused by collisions of the free electrons within
the atomic structure of the resistive materiql. When a collision occurs, heat is given
off; and the electron loses some of its acquired energy.
After completing this section, you should be able to
I Explain energy conversion and voltage drop
. Discuss the causeof energy conversion in a circuit
. Define voltage drop
. Explain the relationship between energy conversion and voltage drop
In Figure 4-10, electrons are flowing out of the negative terminal of the battery. They
have acquired energy from the battery and are at their highest energy level at the negative
side of the circuit. As the electrons move through the resistor, they lose energy.The electrons emerging from the upper end of the resistor are at a lower energy level than those
entering the lower end becausesome of the energy they had has been converted to heat.
The drop in energy level of the electrons as they move through the resistor creates a
potential difference, or voltage drop, acrossthe resistor having the polarity shown in Figure 4-10. Notice that the upper end of the resistorin Figure 4-10 is less negative(more
positive) than the lower end.
(-@*6+@-@+@+\
O
I
v
Electrons have lower
energyonpositive
side of circuit.
+
@
t
@
_
n
l
Y
ta.--*t-@+@+*-A
l
@
+
_
| Energy orop
I ir this direction
Electrons have higher
energy on neganve
side of circuit.
OElectron
F I C U R E4 _ 1 0
Electronflow in a simple circuit.
I
P O W E RS U P P L I E S
101
1. What is the basic reason for energy conversion in a resistor?
2. What is a voltagedrop?
r P O W ERS U P P T IE S
In general, s power supply is q device that provides power to u loud. A load is any
electrical device or circuit that is connected to the output of the power supply and
druws currentfrom the supply.
After completing this section, you should be able to
I Discuss power supplies and their characteristics
. Define ampere-hour rating of batteries
. Discuss electronic power supply efficiency
Figure 4-11 shows a block diagram of a power supply with a loading device connected
to it. The load can be anything from a light bulb to a computer. The power supply produces a voltage acrossits two output terminals and provides current through the load, as
indicated in the figure. The product 1V66 is the amount of power produced by the supply and consumedby the load. For a given output voltage (Vour), more current drawn by
the load means more power from the supply.
F I G U R E4 - 1 1
Block diagram of power supply
and Inad.
Power to Ioad = lVour
Power suppliesrange from simple batteriesto regulated electronic circuits where an
accurateoutput voltage is automatically maintained. A battery is a dc power supply that
converts chemical energy into electrical energy.Electronic power supplies normally convert I 10 V ac (alternating current) from a wall outlet into a regulated dc (direct current)
voltage at a level suitable for electronic components.
Ampere-hourRatingsof Batteries
Batteries convert chemical energy into electrical energy. Becauseof their limited source
of chemical energy,batteries have a certain capacity that limits the amount of time over
which they can produce a given power level. This capacity is measuredin ampere-hours
(Ah). The ampere-hour rating determinesthe length of time that a battery can deliver a
certain amount of current to a load at the rated voltage.
A rating of one ampere-hourmeansthat a battery can deliver one ampereof cunent
to a load for one hour at the rated voltage output. This same battery can deliver two
amperesfor one-half hour. The more cunent the battery is required to deliver, the shorter
is the life of the battery. In practice, a battery usually is rated for a specified current level
'70
lth at
and output voltage. For example, a l2Y automobile battery may be rated for
3.5 A. This means that it can produce 3.5 A for 20 h at the rated voltage.
rl
1O2 I
ENERCYAND POWER
EXAMPLE 4-B
For how manyhourscan a batterydeliver2 A if it is ratedat 70 Ah?
Solution The ampere-hour
ratingis the currenttimesthe numberof hours1x7.
70 Ah = (2 AXx h)
Solvingfor the numberof hours,a yields
,=
70 Ah
=J5n
2A
RelatedProhlem A certainbatterydelivers10A for 6 h. What is its Ah rating?
Efficiencyof ElectronicPowerSupplies
An important characteristic of electronic power supplies is efficiency. Efficiency is the
ratio of the output power to the input power.
Erncrencv
'
output power
input power
- {our
Efficiencv
'
PrN
(4-6)
Efficiency is often expressedas a percentage.For example, if the input power is 100 W
and the output power is 50 W, the efficiency is (50 W100 W) x 1007o= 507o.
All electronic power supplies require that power be put into them. For example, an
electronic power supply generally uses the ac power from a wall outlet as its input. Its
output is usually a regulated dc voltage. The output power is always less than the input
power becausesome of the total power must be used internally to operatethe power supply circuitry. This amount is normally called thepower loss.The output power is the input
power minus the amount of internal power loss.
PouT=Ptoc-Ploss
(4-7)
High efficiency means that little power is lost and there is a higher proportion of output
power for a given input power.
EXAMPLE 4-9
A certainelectronicpowersupplyunit requires25 W of input power.It canproducean
outputpowerof 20 W. What is its efficiency,andwhat is the powerloss?
solution
Efficiency
' \=Pf*-)roo
,^/
E"= (4Y-\t00vo = 80vo
\2swl
Pr-oss= PN - Pour = 25 W - 20 W = 5 W
Related Problem
Pour?
A power supply has an efficiency of 927o.If P61is 50 W, what is
TECHNOLOGY
THEORYINTO PRACTICEI
103
When a loading device draws an increased amount of current from a power supply,
does this change represent a greater or a smaller load on the supply?
,, A power supply produces an output voltage of 10 V. If the
supply provides 0.5 A to
a load, what is the power to a load?
3. If a battery has an ampere-hour rating of 100 Ah, how long can it provide 5 A to a
load?
4. If the banery in Question 3 is a I2Y device, what is its power to a load for the specified value of current?
5. An electronic power supply used in the lab operates with an input power of 1 W. It
can provide an output power of 750 mW. What is its effrciency? Determine the
power loss.
r TECHnology
Theory Into Practice
In this TECH TIP section,the resistancebox that you m.odifiedin Chapter3 is back
on your bench.The last time,you verifiedthat all the resistorvqlueswerecorrect.
This timeyou must makesure eachresistorhas a sufficientpower ratingl and if the
powerrating is insufficient,replacethe resistorwith one that is adequate.
PowerRatings
Assume the power rating of each resistor in the resistancebox as modified in Chapter 3
is % W. The box is shown in Figure 4-12.
(a) Top view
F I G U R E4 - 1 2
I
Determine if the power rating of each resistor is adequate for a maximum of 4 V.
r If a rating is not adequate,determine the lowest rating required to handle the maximum power. Choose from standardratings of t/qW, t/zW, I W. 2 W and 5 W.
Add the power rating of each resistor to the schematic developedin Chapter 3.
IO4 T
ENERCY
A N D POWER
sEcTtoN4-6
1. How many resistors were replaced becauseof inadequatepower ratings?
REVIEW
2. lf the resistancemust operatewith l0 V maximum. which resistorsmust be
changed and to what minimum power ratings?
r SUMMARY
I The power rating in watts of a resistor determinesthe maximum power that it can handle safely.
I Resistors with a larger physical size can dissipate more power in the form of heat than smaller
ones.
r A resistor should have a power rating higher than the maximum power that it is expectedto handle in the circuit.
I Power rating is not related to resistancevalue.
I A resistor normally opens when it burns out.
r Energy is the ability to do work and is equal to power multiplied by time.
r The kilowatt-hour is a unit of energy.
r One kilowatt-hour equals one thousandwatts used for one hour or any other combination of watts
and hours that has a product of one.
I A power supply is an energy source used to operate electrical and electronic devices.
I A battery is one type of power supply that converts chemical energy into electrical energy.
r An electronic power supply converts commercial energy (ac from the power company) to regulated dc at various voltage levels.
I The output power of a supply is the output voltage times the load current.
r A load is a device that draws current from the power supply.
I The capacity of a battery is measuredin ampere-hours(Ah).
r One ampere-hourequals one ampereused for one hour, or any other combination of amperesand
hours that has a product of one.
r A circuit with a high efficiency wastes less power than one with a lower efliciency.
r CIOSSARY
Theseterms are also in the end-of-book glossary.
Ampere-hour rating A number given in ampere-hours(Ah) determined by multiplying the current (A) times the length of time (h) a battery can deliver that current to a load.
Efficiency
Energy
The ratio of the output power to the input power of a circuit, expressedas a percent.
The ability to do work.
The unit of energy.
Joule $
Kilowatt-hour (kWh) A common unit of energy used mainly by utility companies.
Power
The rate of energy usage.
Power rating The maximum amount of power that a resistor can dissipate without being damaged by excessiveheat buildup.
Voltage drop The drop in energy level through a resistor.
Watt (W) The unit of power. One watt is the power when 1 J of energy is used in I s.
Watt's law
r FORMULAS
A law that statesthe relationships of power to curent, voltage, and resistance.
(4-r)
P=Y
Power equals energy divided by time.
(4-2)
W=Pt
Energy equalspower multiplied by time.
(4-3)
P=I2R
Power equals cunent squaredtimes resistance,
(4-4)
P=VI
Power equals voltage times current.
t
SELF-TESTI
r SELF.TEST
1 05
r/2
(4-s)
D - ,
(4-6)
Efficiency =
Power supply efficiency
(4-7)
*
Pour=Pm-Ploss
Output power is input power lesspower loss.
Power equals voltage squareddivided by resistance.
R
1. Power can be definedas
(a) energy
3.
4.
6.
7.
8.
9.
(b) heat
(c) the rate at which energyis used
(d) the time requiredto useenergy
joules
Two hundred
of energyareconsumed
in 10 s. Thepoweris
(a) 2000W
(b) 10w
(c) 20W
(d) 2w
If it takes300ms to use10,000J of energy,
thepoweris
(a) 33.3kw
(b) 33.3w
(c) 33.3mW
In 50 kW, thereare
(a) 500W
(b) 5000w
(c) 0.5 MW
(d) 50,000w
In 0.045W, thereare
(a) 45 kw
(b) 45 mW
(c) 4,500pW
(d) 0.00045Mw
For l0 V and50 mA. thepoweris
(a) 500mW
(b) 0.5W
(c) 500,000pW
(d) answers
(a),(b),and(c)
Whenthecurrentthrougha l0 kQ resistoris 10 mA, thepoweris
(a) 1 w
(b) 10w
(c) 100mW
(d) 1000pW
A2.2kO resistor
dissipates
0.5W Thecurrentis
(a) 15.1mA
(b) 0.227mA
(c) 1.1mA
(d) 4.4mA
A 330Q resistordissipates
2 W. The voltageis
(a) 2.57Y
(b) 660V
(c) 6.6V
(d) 2s,7v
10. If you used500 W of power for 24 h, you have used
(a) 0.5 kWh
(b) 2400 kwh
(c) 12,000kWh
(d) 12 kwh
1 1 . How many watt-hoursrepresent75 W usedfor 10 h?
(a) 75 Wh
t2.
(b) 7s0 wh
(c) 0.75 Wh
(d) 7s00 wh
A 100 O resistormust carry a maximum cunent of 35 mA. Its rating should be at least
(a) 35 W
(b) 35 mW
(c) 123 mW
(d) 3500 mW
13. The power rating of a resistorthat is to handleup to 1.1 W should be
(a)0.25W
(b)1w
(c)2w
(d)5w
t4. A 22 Q half-watt resistor and a 220 O half-watt resistorare connectedacrossa 10 V source.
Which one(s)will overheat?
@) 22 A
$) 220 O
(c) both
(d) neither
15. When the needle of an analog ohmmeter indicates infinity, the resistor being measuredis
(a) overheated
(b) shorted
(c) open
(d) reversed
16. A, 12V batteryis connectedto a 600 Q 1oad.Under theseconditions,it is rated at 50 Ah. How
long can it supply curent to the load?
(a) 2500 h
(b) s0 h
(c) 25 h
(d) 4.16 h
17. A given power supply is capable of providing 8 A for 2.5 h. Its ampere-hourrating is
(a) 2.5 Ah
(b) 20 Ah
(c) 8 Ah
18. A power supply produces a 0.5 W output with an input of 0.6 W Its percentage of efficiency is
(a) 50Va
(b) 60E"
(c) 83.37o
\d) 457o
FI
106 r
AND POWER
ENERCY
r PROBLEMS
More dfficult problems are indicated by an asterisk (*).
SECTION4-1
EnergYand Power
1.. What is the power when energy is consumed at the rate of 350 J/s?
2. How many watts are used when 7500 J of energy are consumed in 5 h?
3. How many watts does 1000 J in 50 ms equal?
4. Convert the following to kilowatts:
(a) 1000w
(b) 37s0w
(d) 50'000w
(c) 160W
5. Convert the following to megawatts:
(b) 3 x 106w
(a) 1,000,000w
(c) 15 x 107w
(d) 8700kw
6. Convert the following to milliwatts:
(a) 1 W
(b) 0.4w
(c) 0'002W
(d) 0'0125
w
7. Convert the following to microwatts:
(c) 0.25 mW
(b) 0.0005 w
(a) 2 W
(d) 0'00667 mW
8. Convert the following to watts:
(d) 9000 pW
(c) 350 mW
power.
If it runs fot 24 h, how many joules of
mW
of
100
uses
9. A particular electronic device
it
consume?
does
energy
*10. A certain appliance uses 300 W. If it is allowed to run continuously for 30 days' how many
kilowatt-hours of energy does it consume?
* 1 1 . At the end of a 31 day period, your utility bill shows that you have used 1500 kwh. what is
(a) 1.5 kW
(b) 0.s Mw
your averagedaily power?
12. Convert 5 x 106watt-minutes to kWh'
13. Convert 6700 watt-secondsto kWh.
14. For how many secondsmust there be 5 A ofcurrent through a 47 C) resistor in order to consume 25 J?
SECTION4-2 Powerin an ElectricCircuit
15. If a 75 V source is supplying 2 Ato a load, what is the resistancevalue of the load?
16. If a resistor has 5.5 V acrossit and 3 mA through it, what is the power?
17. An electric heater works on 120 V and draws 3 A of current. How much power does it use?
18. How much power is produced by 500 mA of current through a 4.7 kQ resistor?
19. Calculate the power handled by a 10 kC) resistor carrying 100 pA'
20. If there are 60 V across a 680 O resistor, what is the power?
21. A 56 f,) resistor is connected acrossthe terminals of a 1.5 V battery. What is the power dissipation in the resistor?
, 7 If a resistor is to carry 2 A of current and handle 100 W of poweq how many ohms must it
be? Assume that the voltage can be adjusted to any required value'
source is connectedacross a 10 Q resistor.
(a) How much energy is used in two minutes?
(b) If the resistor is disconnected after one minute, is the power greater than. less than, or
equal to the power during the two minute interval?
23. A, l2V
SECTION,l-3
ResistorPowerRatings
24. A 6.8 kQ resistor has burned out in a circuit. You must replace it with another resistor with
the same resistance value. If the resistor carries 10 mA, what should its power rating be?
Assume that you have available resistors in all the standardpower ratings.
2 5 . A c e r t a i n t y p e o f p o w e r r e s i s t o r c o m e s i n t h e f o l l o w i n g r a t i n g s : 3 5wW 8 W , 1 2 W 2 0 w .
your particular application requires a resistor that can handle approximately 8 W. Which rating would you use?WhY?
I 1o7
ANSWERS
TO SECTION
REVIEWS
SECTION4-4
EnergyConversionand VoltageDrop in Resistance
26. For each circuit in Figure 4-13, assign the proper polarity for the voltage drop across the
resistor.
(b)
(c)
F I G U R E4 - 1 3
SECTION 4*5
Power Supplies
27,
28.
29.
30.
31.
A 50 Cl load usesI W of power.What is the outputvoltageof the powersupply?
A batterycanprovideI .5 A of currentfor 24 h. What is its ampere-hour
rating?
How muchcontinuouscuffentcanbe drawnfrom an 80 Ah batteryfor l0 h?
If a batteryis ratedat 650 mAh, how muchcurrentwill it providefor 48 h?
If the input poweris 500 mw and the outputpoweris 400 mw, how much poweris lost?
What is the efficiencyof this powersupply?
32. To operateat 85Vaefficiency,how much outputpowermust a sourceproduceif the input
poweris 5 W?
*33. A certainpowersupplyprovidesa continuous2 W to a load.It is operatingat 60Voefficiency.
In a 24 h period,how manykilowatt-hoursdoesthe powersupplyuse?
EWB Troubleshooting and Analysis
Theseproblemsrequireyour EWBcompactdisk.
34. Openfile PRO04-34.EWB
anddeterminethe current,voltage,andresistance.
Usingthe measuredvalues,calculatethe power.
35. Openflle PRO04-35.EWB
and determinethe currentvoltage,and resistance.
Calculatethe
powerfrom thesevalues.
36. Openfile PRO04-36.EW8.
Measurethe currentin thelamp anddetermineif the valueagrees
with that determinedusingthe powerandvoltageratingof the lamp.
ANSWERS
TO SECTION
REVIEWS
Section4-1
1..Poweris the rateat which energyis used.
2.P=Wt
3. Wattis the unit of power.Onewatt is the powerwhen 1 J of energyis usedin 1 s.
a. (a)68,000W=68kW (b) 0.005W=5mW
(c)0.000025W=25prW
5. W = (0.1kW) (10h) = 1 1ry6
6. 2000Wh = 2 kWh
7. 360,000ws = 0.1 kWh
Section 4-2
1 .p = ( 1 0 v ) ( 3 A ) = 3 0 W
2, p = (24 V)(50 mA) = l.zW;1.2 W; the valuesare the samebecauseall energygeneratedby the
source is dissipatedby the resistance.
1OB T
ENERCY
AND POWER
r. P = (5 A)'z(56O) = 1400W
4. p = (20 mA)2(43kA) = 1.33y7
5 . P = ( 5 D 2 / 1 0 c=
, 2.5W
6. P = (8 V)2D.2kO = 29.1mW
7. R =75 w(0.5 A)2= 300A
Section 4-3
l. Resistorshaveresistance
anda powerrating.
2. Alarger surfaceareaof a resistordissipates
morepower.
3.0.125W0.25W0.5W1W
4. A 0.5 W rating shouldbe usedfor 0.3 W.
Section 4-4
1. Energyconversionin a resistoris causedby collisionsof the free electronswithin the
structure.
2. A voltagedrop is the potentialdifferencebetweentwo pointsdueto energyconversion.
Section 4-5
1. More cunentmeansa greaterload.
2 . p = ( 1 0v ) ( 0 . 5 A ) = s w
3. /=l00Ah/5A=20h
4.P=(12V)(sA)=60w
5. Etr = (0.75W/l W)|jOVo= 75Va;Pross= 1000mW - 750mW = 250mW
Section 4-6
1. Two
r ANSWERS
TO RELATED
PROBLEMS
FOR
EXAMPLES
4-r
4-2
4:3
4-4
4-5
4-6
4-7
4-8
4-9
r ANSWERS
TO SEIF.TEST
l . (cl
9. (d)
17. (b)
2. l0 O, 10W; 100Q, 1 W; 400 Q. 74W
3000J
(a) 0.001W
(b) 0.0018w
(c) 1 w
2 kwh
(a) 40 w
(b) 376w
(c) 625mW
60 W
0.5W
Yes
60Ah
46W
2. (c)
10. (d)
18. (c)
3.(a)
11. (b)
4.(d)
12. (c)
(d) 0.000001w
s. (b)
13. (c)
6. (d)
14. (a)
7. (.a)
15. (c)
8. (a)
16. (a)