## 7.5 Electrical Energy

Definition of electrical energy,E and the S.I. unit.

Based on the definition of current,,

Q = It …………………(1)

Based on the definition of potential difference,

E = V Q ………………(2)

Substitute (1) into (2)

E = VIt …………………(3)

So the definition of ” electrical energy is the product of the potential difference , the current and the time.”

The S.I. unit of Electrical energy is Joule (J)

I J = 1 V A s

Based on the equation of the Ohm’s law

V = IR …………………..(4)

……………………(5)

Substitute (4) into (3)

E = I2 R t

Substitute (5) into (3)

Conclusion:

Example 1

A current of 5A flows in a heating elements for 10 minutes. If the potential difference across the elements is 240 V, calculate the electrical energy is used by the elements

Solution

Example 2

When the switch S is closed for 5 minutes , calculate the energy is produced in the resistor 6W?

Solution

The definition of the Electrical Power ,P and the S.I. unit

From the definition of power,

and from the formula of the electrical energy ,

E = V It or E = I2 Rt or

or or

Conclusion

The S.I. unit f power is Watt

1 W = 1 V A

Example 3

A small laboratory immersion heater uses a 12 supply. The current through the heater is 4A. What is the power of the heater.

Solution

Example 4

An electric kettle is labelled 3 kW,240 V.

(a) What is meant by the label 3KW,240 V?

(b) What is the current flows through the kettle?

(c) Determine the suitable fuse to use in the kettle.

(d) Determine the resistance of the heating elements in the kettle.

Solution

Experiment to determine the power of a bulb.

The switch is closed.

The reading of the ammeter = I and the voltmeter V is recorded.

The power of the bulb is calculated by using the formula P = VI

The experiment is repeated 5 times by adjusting the rheostat.

The average power of the bulb is calculated.

Every house has an electrical meter supplied by the Electricity board.

The units used are kilowatt-hours (kWh).

1 kilowatt – hour is the energy supplied in 1 hour to an appliance whose power rating is 1 kW.

1 kW j = 1000 x 3600 J = 3.6 x 106 J

Example 4

Determine how many units is used for the following electrical appliances :

(a) 2 bulbs is used in 5 hours and each is labelled 60 W,240V

(b) An air-conditioner is rating 2kW and is used for 5 hours per day during one month

Solution

Example 6

The following table shows the electrical appliances is used at Ahmad’s house.

 Appliance Number of appliance Power of each appliance Time is used for a day (Hour)) Fluorescent lamp 15 60 12 Fan 8 90 5 Iron 1 1200 0.5

Calculate the cost of using the electrical appliances by Ahmad’s Family within 20 days.

[ The cost of electricity is 20 sen for first 100 units and

24 sen for next 900 units ]

Solution

Efficiency of Electrical Appliances

Example 7

An electric motor is used to lift a load of mass 2 kg to a height 5 m in 2.5 s. If the supply voltage is 12 V and the flow of current in the motor is 5.0 A , calculate

(a) Energy input to the motor

(b) Useful energy output of the motor

(c) Efficiency of the motor

Solution

Example 8

An electric kettle is used to boil some water to make tea. The kettle has a power rating of 3 kW, and is filled with 0.5 kg of cold tap water at 20oC . It takes a minutes and a half to boil. How efficient is this kettle?

[ Specific heat capacity of water = 4 200 Jkg-1 oC-1]

Solution

Ways of increasing energy efficiency.

(1) Maintaining the electrical appliances in good working condition.

For example :

Regularly cleaning and removing dust from the air filters of air conditioners and blades of electric fans.

Cleaning regularly filter bags of vacuum cleaner.

(2) Operating the appliances correctly.

For example :

Turn off the appliance when not in use.

Use full loads of washing in a washing machine.

Use free wind and sunshine instead of a tumble-dryer whenever possible.

Do not put warm food into a fridge or freezer.

Do not put more water in a kettle than you need for your hot drinks.

Switch off all unnecessary lights; use low-power lamps and install fluorescent lighting

where it is acceptable.

Make full use of energy needed to heat an oven by cooking several things at the same time.