##### The Cost of Electrical Energy

The power and voltage rating of home electrical appliances

1. Electricity is just one form of energy. When we pay for electricity, we are charged for the amount of electrical energy we have converted into other forms.

2. Electricity is sold in energy unit kilowatt-hour (kWH). The number of kilowatt-hour you use at home is measured by the electricity meter. Photograph 8.1 shows an example of such a meter.

3. Different electrical appliances use different amounts of electrical energy. The rate at which an appliances uses energy is called power, and this is measured in watts (joules per second).

$$Power,\ P=\frac { Electrical\ energy,\ E }{ time,\ t }$$

$$1\ watt\ (W)\ =\ 1\ J{ s }^{ -1 }$$

Calculating the amount of current flowing through an electrical appliance

1. The voltage and power ratings marked on appliances allow you to calculate the operating current using the equation:

$$Power\ (W)=voltage\ (V)\ \times \ current\ (A)\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P=VI\\$$

2. Table below shows some examples of the home electrical appliances together with their power and voltage ratings. The amount of current flowing through each appliance is shown in the last column.

 Appliance (operating at 240 V) Power rating, P (W) Operating current, / (A) Light bulb 60 0.25 Television set 200 0.83 Refrigerator 500 2.10 Toaster 1000 4.17 Electric kettle 2000 8.33 Hair dryer 1500 6.25 Personal computer 100 0.42 Table fan 50 0.21

Relationship between electrical energy usage, power and time

1. The power rating of an appliance is related to the electrical energy usage and time by the following formula:

$$Power,\ P=\frac { Electrical\ energy,\ E }{ Time,\ t }$$

Thus, $$Electrical \ energy,\ E=\ power,\ P\ \times\ time,\ t$$

Calculating the cost of electrical energy used

1. Electrical energy used at home is measured by the joule meter. The cost of electrical energy used is based on the number of kilowatt-hours (kWh) used.

2. One kilowatt-hour (1 kWh) is the electrical energy used by a device a rate of 1000 watts in one hour.

$$Electrical\ energy\ (kWh)=Power\ (kW)\ \times\ Time\ (h)$$

$$1\ kWh=1\ kW \times 1\ h\\ \quad \quad \ =1000\ W\times 60\times 60\ s\\ \quad \quad \ =1000\ J\ { s }^{ -1 }\times 3600\ s\\ \quad \quad \ =3.6\times { 10 }^{ 6 }\ J$$

3. The cost of electrical energy used per month can be determined as follows:

$$Cost\ of\ electrical\ energy\ consumption \ \\\\= Total\ domestic\ units\ \times\ Tariff\ rate$$