Physics 30 Lesson 30 Electric Power and Energy
I Electric power
From Lesson 25 (Energy, Work and Power) we know that power is work / time:
P = W units: = W (watts)
t s
and sin!e W = energy
P = energy
t
"rom Lesson #$ (E%e!tri! potentia%) we know that energy = V q there"ore power
!an &e determined &y
P = ' (
t
"rom Lesson #2 (E%e!tri! !urrent) we know that ) = (
t
P = ' ( = ' )
t
E%e!tri! power is determined &y using the "ormu%a:
P = ' )
units: W (watts)
Example 1
*n e%e!tri! toaster *n e%e!tri! toaster uses #5+$ * "rom a #2$ ' %ine+ What is the power
!onsumed &y the toaster when it operates,
P = ' ) = #2$ ' (#5+$ *) = 1800 W = 1.80 kW
-he power e(uation !an a%so &e !om&ined with .hm/s Law to deri0e two other power
e(uations:
) = '
1
P = ' ) = ' ' = '
2
P = '
2
1 1 1
' = ) 1
P = ' ) = () 1) ) = )
2
1 P = )
2
1
2$ 3 #
Example 2
What is the resistan!e o" a !ir!uit that in!%udes a toaster that !onsumes #+$ kW o"
power on a #2$ ' %ine,
P = '
2
1 = '
2
= (#2$ ')
2
= 1.
1 P #$$$ W
Example 3
What power is !onsumed when a 5$$ resistor draws a !urrent o" #$+$ *,
P = )
2
1 = (#$+$ *)
2
(5$$ ) = !0.0 kW
II Electric energy
From Lesson #$ we know that
E = ( '
4owe0er, "or e%e!tri! !ir!uits we usua%%y do not re"er to the amount o" !harge passing
through it, rather we ta%k a&out the amount o" !urrent gi0en+ We know that ( = ) t
there"ore
E = ( ' = () t)' E = ' ) t
Example 4
What energy is stored in a 5+$ ' &attery that !an de%i0er a !urrent o" 5+$ m* "or 2$
minutes,
E = ' ) t = 5+$ ' (5+$ 6 #$
32
*) (2$ 6 7$ s) = ! "
*n a%ternati0e unit o" energy to the ou%e is "ormed i" we ha0e the power in ki%owatts
(kW) and the time in hours (h)+
E = P t = kWh (ki%owatthour)
(# kWh = 2+7 6 #$
7
)
#ote$ % kilowatt&ho'r is a 'nit o( energy) not power.
2$ 3 2
Example 5
What energy in ou%es and kWh is !onsumed &y a 5$$ W toaster that operates "or 2$
minutes,
E = P t = 5$$ W (2$ 6 7$ s) = *00 k"
E = P t = $+5$$ kW (2$/7$ h) = 0.1*+ kWh
III ,ost o( electrical energy
When e%e!tri! power !ompanies !harge "or e%e!tri!a% power they !harge a !ertain
amount "or ea!h kWh o" energy+ )" a rate is gi0en either as a !ost/ou%e or !ost/kWh,
then you must use the appropriate units in the !a%!u%ation+
Example 6
* toaster with a resistan!e o" #$+$ is !onne!ted to a #2$ ' %ine+ )" the toaster
operates "or 2$ minutes per day, what is the !ost o" operating the toaster "or one year in
an area where the e%e!tri!a% energy !osts 8 $+$7$ / 9,
P = '
2
= (#2$ ')
2
= #::$ W
1 #$+$
E = P t = #::$ W (2$ min/day 6 7$ s/min 6 275 days) = 5:7+# 9 (year)
!ost = rate 6 energy = 8 $+$7$ / 9 6 5:7+# 9 = - !+ (per year)
Example 7
*n app%ian!e draws #5 * "rom a #2$ ' %ine+ )" the app%ian!e operates 5+$ h/day, si6
days a week, "or 5$ weeks per year, what is the !ost o" operating the app%ian!e "or one
year i" e%e!tri!a% energy !osts 8 $+$5$ / kWh,
P = ' ) = #2$ ' (#5 *) = #;$$ W = #+; kW
E = P t = #+; kW (5+$ h/day)(7 days/week)(5$ weeks) = 2<$$ kWh
!ost = rate 6 energy = 8 $+$5$ / kWh 6 2<$$ kWh = - 13!.00
2$ 3 2
IV Practice pro.le/s
#+ What is the power output o" a =.>? wa%kman whi!h runs on two #+5 ' &atteries
!onne!ted in series and draws #+5$ m* o" !urrent, (:+5 mW)
2+ * !ertain app%ian!e has a resistan!e o" #5+$ and runs on a #2$ ' %ine+ 4ow
mu!h energy is re(uired to run this app%ian!e "or 2+$ h, (#+52 kWh)
2+ )" the !ost o" e%e!tri! power is 8 $+$7$ / kWh, !a%!u%ate the !ost o" running a
spot%ight whi!h draws 2+22 * at #2$ ' "or 2+$ h a day "or 2$ days+ (8#+::)
2$ 3 :
Lesson 1 0and&in assign/ent
#+ What power !ompany supp%ies power to the @a%gary area, 4ow mu!h do they
!urrent%y !harge per kWh o" e%e!tri!a% energy,
2+ @a%!u%ate the e%e!tri!a% energy dissipated in #+5 min when there is a !urrent o"
:+$* through a potentia% di""eren!e o" 7$ '+ (2+2 6 #$
:
)
2+ @a%!u%ate the power dissipated &y ea!h o" the "o%%owing %oads+
a) a !%othes dryer drawing #2+5 * "rom a 2:$ ' sour!e (2+$$ 6 #$
2
W)
&) a kett%e that draws #2+$ * and has a resistan!e o" ;+2 (#+2 6 #$
2
W)
!) a 2:$ heating pad p%ugged into a #2$ ' sour!e (7$+$ W)
:+
a) What ma6imum power !an &e used on a 2:$ ' !ir!uit with a #5 * "use,
(2+7$ kW)
&) 4ow mu!h more !urrent !an sa"e%y &e drawn "rom a #2$ ' out%et "used at
2$ * i" an ;$$ W toaster and an ##;$ W kett%e are a%ready operating in the
!ir!uit, (2+5 *)
5+ * #+$ kW toaster, designed to operate a #2$ ', is mistaken%y !onne!ted to a
sour!e o" 2:$ '+
a) What !urrent is the toaster designed to draw, (;+2 *)
&) What !urrent wi%% draw when !onne!ted to 2:$ ', (#< *)
!) What power wi%% it use on 2:$ ', and what wi%% &e the %ike%y resu%t, (:+# kW)
7+ * re"rigerator !ompressor draws 2+5 * "rom a #2$ ' sour!e and operates "or an
a0erage o" #5 min out o" ea!h hour+ @a%!u%ate the annua% !ost o" operating the
re"rigerator i" the a0erage !ost o" e%e!tri!a% energy is 8$+$:2/kW
.
h+ (82<+55)
<+ *n e%e!tri! heater has a resistan!e o" #7 when operating on a #2$ ' %ine+ )" the
!ost o" e%e!tri!a% energy is 8 $+$2$/9, how mu!h does it !ost to operate "or 2$
minutes, (8$+$:5)
;+ *n e%e!tri! %awn mower has a resistan!e o" #7$ and draws #5 *+ What is the
!ost o" operating the %awn mower "or 2$ minutes i" e%e!tri!a% energy !osts
8 $+#2/kWh, (82+#7)
5+ )n a town, e%e!tri!a% energy !osts 8 $+$:$ / kWh+ * modern kerosene %amp
produ!es a&out the same amount o" %ight as one #$$ watt %ight &u%& &ut uses
22+; mL o" "ue% per hour+ )" kerosene !osts 8 $+22 / L, how mu!h money is sa0ed i"
a #$$ W &u%& is used o0er a 2$$$ hour period o" time, (87+:2)
2$ 3 5
#$+ )" the !ir!uit &e%ow is !onne!ted to a power sour!e o" #2$ ' "or 27 days, what is
the !ost o" operating the !ir!uit i" the !ost o" e%e!tri!a% energy is 8 $+#2 / 9,
(82;<+7$)
##+ 4ot water in a domesti! residen!e is produ!ed &y heating water in a tank+ -he
heating sour!e in many hot water tanks is pro0ided &y 22$ ' e%e!tri!a% !oi%s that
are p%a!ed in the tank+ Ea!h o" the !oi%s has a resistan!e o" #5 +
a+ Asing the sym&o%s a&o0e, draw the !ir!uit diagram that wou%d use two !oi%s
to heat the water in the shortest possi&%e time+
&+ What !urrent is pro0ided &y the 22$ ' sour!e to the heating !oi%s,
!+ What is the power !onsumed &y ea!h heating !oi%,
d+ )" you wanted to measure the !urrent and potentia% di""eren!e a!ross one o"
the !oi%s, draw in the appropriate meters and how you wou%d hook them in+
e+ -he amount o" energy needed to heat water is gi0en &y the "ormu%a
E = m c T, where m is the mass o" water, c is the spe!i"i! heat !apa!ity o"
water (:+#5 k/(
o
@ kg)), and T is the !hange in temperature+
4ow %ong in minutes wou%d it take "or the two heating !oi%s to raise the
temperature in the tank !ontaining #7$ kg o" water &y #+$
o
@,
2$ 3 7
wire
E%e!tri!a%
sour!e
22$ '
* heating !oi%
2
#: #5
2$
5
