# Measurement of electrical power and energy

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The rate of heating effect is usually measured is power units, i.e., the kilowatt (kW), while the amount of energy converted is usually measured in energy unit, i.e., the kilowatt-hour (kWh).

Power (P) of electrical appliances is given by:

\begin{aligned} P &= I^{2}R \\ &= \frac{V^{2}}{R} \\ &= VI \end{aligned}

where,
V = voltage applied across appliance
I = current flowing through appliance
R = total resistance of appliance

– SI unit for power is the kilowatt (kW)
– 1 W = 1 J s-1 => 1 kW = 1000 W = 1000 J s-1

Energy converted (E) of electrical appliances is given by

\begin{aligned} E &= P \times t \\ &= I^{2}R \: \times \: t \\ &= \frac{V^{2}}{R} \: \times \: t \\ &= VI \: \times \: t \end{aligned}

where,
V = voltage applied across appliance
I = current flowing through appliance
R = total resistance of appliance
t = total time taken

– SI unit for energy conversion is the kilowatt-hour (kWh)
– 1 kWh = (1000 W) X (60 X 60 s) = 3 600 000J = 3600 kJ = 3.6 MJ
– Appliances with high power rating consume more electrical energy per unit time.

Notes:
Many, if not all, electrical appliances are not 100% efficient. Some of the electrical energy are converted to other forms of energy. e.g. light, sound and etc.

Cost of using electrical appliances

• Domestic consumption of electrical energy is measured by electrical meters units of kilowatt-hour (kWh).
• Each consumed energy unit (kWh) is billed according to a fixed or variable rate. The total cost of energy usage for a defined period is the product of number of consumed energy units in kWh and the charge per energy unit.
• At the beginning of each month, the electricity meter of the domestic household is read and the total number of energy units consumed so far is recorded. The difference between last month’s reading and this month’s reading is the current month’s consumption.