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ECE 333 Homework 1 Solutions :: Spring 2010
1.6
A 52gallon electric water heater is designed to deliver 4800 W to an electric resistance heating
element in the tank when it is supplied with 240 V (it doesn't matter if this is ac or dc).
a. What is the resistance of the heating element?
P
!
V
2
R
!
R
!
V
2
P
R
!
240
2
"
V
#
4800
"
W
#
$
R
!
12
"%#
b. How many watts would be delivered if the element is supplied with 208 V instead of 240 V?
P
!
V
2
R
P
!
208
2
"
V
#
12
"%#
$
P
!
3605.33
"
W
#
c. Neglecting any losses from the tank, how long would it take for 4800 W to heat the 52
gallons of water from 60
o
F to 120
o
F?
The conversion between kilowatts of electricity and
Btu/hr of heat is given by 3412 Btu/hr = 1 kW.
Also, one Btu heats 1 lb of water by 1
o
F and 1
gallon of water weighs 8.34 lbs.
T
!
120
o
'
60
o
!
60
o
F
52
gal of H
2
O
$
52
(
8.34
!
433.68
lbs
3412
Btu
)
hr
1
kW
(
4.8
kW
!
16377.6
Btu
)
hr
1
hr
16377
Btu
(
1
Btu
1
lb
1
o
F
(
60
o
F
(
433.68
lbs
!
1.589
hr
1.7
Suppose an automobile batter is modeled as an ideal 12V battery in series with an internal
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 Spring '09
 Overby

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