Core Unit III: Electricity
D. Electric Power and Energy

Key Concepts

In an electric circuit, power is the rate at which energy is used.

The derived unit for power is the watt.

1 watt = 1 joule/second

The following relationships for power in an electric circuit can also be developed:

P = VI

1 watt = 1 volt ^. ampere

     = 1 (joule/coulomb)/(coulomb/second)

     = 1 joule/second, etc.

P = I²R

1 watt = 1 ampere^{2 .} ohm

1 watt = 1 volt²/ohm

The power rating shown on electrical appliances gives a comparative indication of the cost of operating those appliances (not taking efficiencies into account).

The energy consumed by an electrical appliance depends on its power rating and the length of time it is operating.

E = Pt

The joule is too small to measure electrical energy consumption. More common are the megajoule (MJ), or the kilowatt ^. hour (kW ^. h).

1 MJ = 1 x 10⁶ J
          = 1 x 10⁶ W ^. s

1 kW ^. h = 3.6 MJ
               = 3.6 x 10⁶J

The cost of using electricity can be calculated if the amount of energy used is known. (Some physics texts oversimplify this topic. They do not mention anything about base rates and minimum monthly charges which are paid regardless of usage, sliding usage scales, or discount rates paid by industrial and other "power users." To determine accurate costing of electrical rates, check with the utility company. Rates are subject to change from time to time.)

The demand for electrical energy has increased dramatically in recent years.

Conserving electrical energy is important. It saves the consumer money, and reduces the pressure being placed on the environment.

"Discounts" for excessive use are offered by electrical utility companies in some countries, while in other countries users pay a premium for excessive use. These are two different pricing policies.

The production of electricity from various sources differs throughout Canada. Each method used has a particular impact on the environment. Investigate the Saskatchewan scene.

Learning Outcomes

Students will increase their abilities to:

1. Define power.

2. Express the correct units for power.

3. Develop various different relationships for power in an electric circuit.

4. Use a variety of expressions for electrical power to solve problems.

5. Explain how the power rating on electrical appliances can assist a person in making wise decisions as a consumer.

6. Explain why the joule is not normally used as a unit to measure electrical energy consumption.

7. State two common units used to measure electrical energy consumption.

8. Solve problems involving energy in electric circuits.

9. Identify the main ways that are used to produce electric in Canada.

10. Identify the impact each main method used to produce electricity has on the environment.

11. Compare the main methods used to produce electricity in Canada and determine which are likely to be most and least desirable. Debate the choices selected.

12. Suggest alternative methods of producing electricity which may have potential for future development.

13. Understand overloading of circuits in the home (circuit breakers and fuses).

Teaching Suggestions, Activities and Demonstrations

1. Compare the energy used in a given amount of time when using appliances having different power ratings.

2. Have students design and conduct an activity to determine the cost of using electricity for a "typical" household in Saskatchewan over a given amount of time.

3. Connect a power supply to a small electric motor. Connect an ammeter, a voltmeter, and a rheostat to the circuit. Arrange the motor so that it can lift a few small weights vertically. Lift the weights, recording the meter readings and the time it takes to lift the weight. Determine the electrical energy input to the motor: E_(in) = VIt. Calculate the energy output from the motor, based on the change in potential energy of the object being lifted:
   E_(out) = mgh Determine the efficiency of the motor:
   

   Repeat with different loads or different rheostat settings. Determine if the efficiency depends on these factors.

   Disconnect the power supply. Allow the weights to drop to the ground. Take readings from the voltmeter and the ammeter. If a reading is noticed on the meters, speculate as to what is acting as the source of the electromotive force. If a bigger load is used, causing the disconnected motor to spin faster, ask the students to predict and observe what happens to the readings on the voltmeter and the ammeter.

4. Compare the cost of using electricity or the pricing policies in Saskatchewan with that of other provinces or other countries.

5. Compare pricing policies which offer discounts or premiums for increased use. Assess the reasons why those different policies are used.

6. Using an electric calorimeter connected in a circuit, record the change in temperature in the circuit after a certain amount of time. Record current and electric potential readings in the circuit. Determine the electric energy input to the calorimeter and the electric equivalent of heat produced. Compare experimental and accepted values and account for any discrepancies.

   Instead of, or in addition to, an electric calorimeter, a kettle can be used. An interesting comparison of efficiencies can be made for the two types of heating devices.

7. Mount a ten, twelve, or fourteen speed bicycle on a set of rollers or a training stand. (Check with students or other bicycle enthusiasts for this. Alternatively, use a stationary exercise cycle, an ergometer, or even a set of training wheels mounted slightly below the rear wheel.)

   Mount an electric bicycle generator and light assembly to the bicycle. Connect a voltmeter and ammeter to the circuit. Have different students pedal the cycle at their top speed (warming up properly beforehand).

   Take current and electric potential difference readings to determine the maximum electric power produced. Compare this to the way they would have to pedal to sustain a certain power output for a longer period of time. (The average person can put out about 75 watts.)

   If heart rate monitors, stethoscopes, or sphygmomanometers are available, take pulse readings at regular intervals. Monitor blood pressure, skin temperature, or other "vital signs." Use these as possible indicators of aerobic capacity. (Have students research how medical stress tests are performed. Integrate this activity with Physical Education. Visit a local hospital which performs stress tests. Find out how an electrocardiograph or an electroencephalograph works.) This activity could also be tied into the unit on Animal Systems in Biology 30.

   Discuss the energy transformations taking place to produce the electrical energy. If the bicycle can be moved outdoors, perform an activity to determine the work done to ride the bicycle a measured distance along a level surface. (The students can determine how the experiment would have to be designed. This is not a simple activity. Many variables are involved.)