4.4 Electric Power and Energy – includes Heat energy – Douglas College Physics 1207

Probles & Exercises

1: What is the power of a 1.00 x102 MV lightning bolt having a current of 2.00 x 104 A?

2: What power is supplied to the starter motor of a large truck that draws 250 A of current from a 24.0-V battery hookup?

3: A charge of 4.00 C of charge passes through a pocket calculator’s solar cells in 4.00 h. What is the power output, given the calculator’s voltage output is 3.00 V? (See Figure 2.)

4: How many watts does a flashlight that has 6.00 x 102 C pass through it in 0.500 h use if its voltage is 3.00 V?

5: Find the power dissipated in each of these extension cords: (a) an extension cord having a 0.0600 Ω resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of 0.300 Ω

6: Verify that the units of a volt-ampere are watts, as implied by the equation P = IV

7: Show that the units   1 V2 /Ω  = 1 W , as implied by the equation P = V2 / R

8: Show that the units  1 A2 •Ω  = 1 W , as implied by the equation P = I2 R. 

9: Verify the energy unit equivalence that 1 kW•h = 3.60  x 106 J.

10: Electrons in an X-ray tube are accelerated through 1.00 x 102 kV and directed toward a target to produce X-rays. Calculate the power of the electron beam in this tube if it has a current of 15.0 mA.

11: An electric water heater consumes 5.00 kW for 2.00 h per day. What is the cost of running it for one year if electricity costs 12.0 cents per kWh? See the figure below.

12: With a 1200-W toaster, how much electrical energy is needed to make a slice of toast (cooking time = 1 minute)? At 9.00 cents/kW•h, how much does this cost?

13: What would be the maximum cost of a CFL such that the total cost (investment plus operating) would be the same for both CFL and incandescent 60-W bulbs? Assume the cost of the incandescent bulb is 25 cents and that electricity costs 10.0 cents/kW•h. Calculate the cost for 1000 hours, as in the cost effectiveness of CFL example.

14: Some makes of older cars have 6.00-V electrical systems. (a) What is the hot resistance of a 30.0-W headlight in such a car? (b) What current flows through it?

15: Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at 1.00 A•h and 1.58 V keep a 1.00-W flashlight bulb burning?

16: A cauterizer, used to stop bleeding in surgery, puts out 2.00 mA at 15.0 kV. (a) What is its power output? (b) What is the resistance of the path?

17: The average television is said to be on 6 hours per day. Estimate the yearly cost of electricity to operate 100 million TVs, assuming their power consumption averages 150 W and the cost of electricity averages 12.0 cents per kW/h or kW•h.

18: An old lightbulb draws only 50.0 W, rather than its original 60.0 W, due to evaporative thinning of its filament. By what factor is its diameter reduced, assuming uniform thinning along its length? Neglect any effects caused by temperature differences.

19: 00-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries 1.00 x102 A?

20: Integrated Concepts

Cold vaporizers pass a current through water, evaporating it with only a small increase in temperature. One such home device is rated at 3.50 A and utilizes 120 V AC with 95.0% efficiency. (a) What is the vaporization rate in grams per minute? (b) How much water must you put into the vaporizer for 8.00 h of overnight operation? (See Figure 4.)

21: Integrated Concepts

(a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of 1.00 x102 MV, and a length of 1.00 ms? (b) What mass of tree sap could be raised from 18.0ºC to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

22: Integrated Concepts

What current must be produced by a 12.0-V battery-operated bottle warmer in order to heat 75.0 g of glass, 250 g of baby formula, and 300 g  of aluminum from 20.0ºC to 90.0ºC in 5.00 min?  (Find your final answer to 3 significant figures) Specific heat capacities in J/kg oC can be found earlier.  c water = 4186 c baby food = 3999 c aluminum = 900 c glass = 888 J/kg oC.

23: Integrated Concepts

How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from 37.0ºC to 100ºC and then boil away 0.500 g of water, if it puts out 2.00 mA at 15.0 kV? Ignore heat transfer to the surroundings.

24: Integrated Concepts

24: Hydroelectric generators (see Figure 5) at Hoover Dam produce a maximum current of 8.00 x 103 A  at 250 kV. (a) What is the power output? (b) The water that powers the generators enters and leaves the system at low speed (thus its kinetic energy does not change) but loses 160 m in altitude. How many cubic meters per second are needed, assuming 85.0% efficiency?

25: Integrated Concepts

(a) Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0-V batteries of a 750-kg electric car be able to supply: (a) To accelerate from rest to 25.0 m/s in 1.00 min? (b) To climb a 2.00 x102 m high hill in 2.00 min at a constant 25.0-m/s speed while exerting 5.00 x 102 N  of force to overcome air resistance and friction? (c) To travel at a constant 25.0-m/s speed, exerting a 5.00 x 102 N force to overcome air resistance and friction for another 2.00 minutes? See Figure 6.

26: Integrated Concepts

A light-rail commuter train draws 630 A of 650-V DC electricity when accelerating. (a) What is its power consumption rate in kilowatts? (b) How long does it take to reach 20.0 m/s starting from rest if its loaded mass is  5.30 x 104 kg, assuming 95.0% efficiency and constant power? (c) Find its average acceleration. (d) Discuss how the acceleration you found for the light-rail train compares to what might be typical for an automobile.

27: Integrated Concepts

(a) An aluminum power transmission line has a resistance of  0.0580 Ω/ km. What is its mass per kilometre? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

28: Integrated Concepts

(a) An immersion heater utilizing 120 V can raise the temperature of a 100 gram aluminum cup containing 350 grams of water from 20.0ºC to 95.0ºC in 2.00 min. Find its resistance, assuming it is constant during the process. (b) A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

29: Integrated Concepts

(a) What is the cost of heating a hot tub containing 1500 kg of water from 10.0ºC to 40.0ºC, assuming 75.0% efficiency to account for heat transfer to the surroundings? The cost of electricity is 9.00 cents per kWh (b) What current was used by the 220-V AC electric heater, if this took 4.00 h?

30: Unreasonable Results

(a) What current is needed to transmit 100 MW of power at 480 V? (b) What power is dissipated by the transmission lines if they have a 1.00 Ω resistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?

31: Unreasonable Results

(a) What current is needed to transmit 100 MW of power at 10.0 kV? (b) Find the resistance of 1.00 km of wire that would cause a 0.0100% power loss. (c) What is the diameter of a 1.00-km-long copper wire having this resistance? (d) What is unreasonable about these results? (e) Which assumptions are unreasonable, or which premises are inconsistent?

32: Construct Your Own Problem

Consider an electric immersion heater used to heat a cup of water to make tea. Construct a problem in which you calculate the needed resistance of the heater so that it increases the temperature of the water and cup in a reasonable amount of time. Also calculate the cost of the electrical energy used in your process. Among the things to be considered are the voltage used, the masses and heat capacities involved, heat losses, and the time over which the heating takes place. Your instructor may wish for you to consider a thermal safety switch (perhaps bimetallic) that will halt the process before damaging temperatures are reached in the immersion unit.