Physics 202 Homework, Day 12: Chapter 17: #25,33,34,36,45
ü 25. A certain light bulb has a tungsten filament having a resistance of 15W at 20°C, and 160W when hot.
Assume that the equation R = R0 @ 1 + aHT - T0 LD can be used over the large temperature range here. Find
the temperature of the filament when it is hot.
R = R0 @ 1 + aHT - T0 LD =>
R
R0
1
R
- 1 = aHT - T0L => a @ R0 - 1] + T0
R0 = 15.; R = 160.; a = 4.5 * 10-3 ; T0 = 20.; T =
1
R
a
R0
- 1 + T0; Print@"Temperature = ", T, " °C"D
NSolve@R ã R0 H1 + a HT - T0LL, TD
Temperature = 2168.15 °C
88<<
ü 33. Suppose your waffle iron is rated at 1.00 kW when connected to a 120 V source.
(a) What current does the waffle iron carry?
(b) What is its resistance?
Power = I V => I =
P
V
power = 1000.; voltage = 120.; current =
power
voltage
; Print@"Current = ", current, " Amperes"D
Current = 8.33333 Amperes
R=
V
I
resistance =
voltage
current
; Print@"Resistance = ", resistance, " Ohms"D
Resistance = 14.4 Ohms
ü 34. If electricity costs 12 cents or $0.12 per kilowatt hour, how much does it cost to
(a) burn a 100 W bulb for 24 h?
(b) Operate an electric oven for 5.0 h if it carries a current of 20.0A at 220 V?
[ 1 kW h = 1000 W x 1 hour ]
(a) 100 W Bulb:
In[63]:=
energy = 0.1 * 24; cost = .12 * energy;
Print@"Energy used = ", energy, " kWh, which costs $", costD
Energy used = 2.4 kWh, which costs $0.288
(b) Oven
In[64]:=
power = H20. * 220.L ê 1000.; hours = 5.; energy = Hpower * hoursL;
cost = .12 * energy; Print@"Energy used = ", energy, " kWh, which costs $", costD
Energy used = 22. kWh, which costs $2.64
ü 36. A high voltage transmission line with a resistance of 0.31 W/km carries a current of 1,000 A. The line is
at a potential of 700,000 V at the power station and carries the current to a city located 160 km from the
station.
(a) What is the power loss from resistance in the line?
(b) What fraction of the trasmitted power does this loss represent?
2
Day_12_sol.nb
36. A high voltage transmission line with a resistance of 0.31 W/km carries a current of 1,000 A. The line is
at a potential of 700,000 V at the power station and carries the current to a city located 160 km from the
station.
(a) What is the power loss from resistance in the line?
(b) What fraction of the trasmitted power does this loss represent?
In[83]:=
distance = 160; resistance = 0.31 * distance; Print@"Resistance = ", resistance, " Ohms"D
powerSupplied = 700 000 * 1000.;
Print@"Power Supplied = ", powerSupplied ê 1 000 000, " Megawatts"D
powerLost = 10002 * resistance; Print@"Power Lost = ", powerLost ê 1 000 000., " Megawatts"D
powerLost
PrintB"Fraction of power lost = ",
, " or about 7%."F
powerSupplied
Resistance = 49.6 Ohms
Power Supplied = 700. Megawatts
Power Lost = 49.6 Megawatts
Fraction of power lost = 0.0708571 or about 7%.
ü 45. An 11 W energy-efficient fluorescent lamp is designed to produce the same illumination as a
conventional 40 W lamp. How much does the energy-efficient lamp save during 100 hours of use? Assume
a cost of $0.08 / kWh for electrical energy.
In[90]:=
energy11W = 11. * 100. ê 1000; Print@"Energy used by 11 W bulb = ", energy11W, " kWh"D
energy40W = 40. * 100. ê 1000; Print@"Energy used by 40 W bulb = ", energy40W, " kWh"D
Print@"Cost savings = $", Henergy40W - energy11WL * .08D
Energy used by 11 W bulb = 1.1 kWh
Energy used by 40 W bulb = 4. kWh
Cost savings = $0.232
ü