# Electrical Power

Electrical power (represented by the letter P in electrical formulae) is defined as the rate at which electrical energy is converted into some other form of energy such as heat, light, sound or motion. The converted electrical power can be used to carry out some kind of work such as heating a room (e.g. using an electric storage heater), providing a source of light (using an electric light bulb), producing sound (using loudspeakers) or driving some electro-mechanical device (such as an electric motor). The Standard International (SI) unit of measurement for electrical power is the watt. Larger units of measurement commonly used include the kilowatt (1 × 103 watts) and the megawatt (1 × 106 watts). A single watt represents the amount of energy (measured in Joules) dissipated in an electrical circuit or device in one second. The amount of electrical energy (in joules) consumed by an electrical appliance in a given period of time is thus calculated by multiplying its power rating (in watts) by the length of time involved (in seconds). Energy that is dissipated by an electrical device or circuit as heat without actually doing any useful work is wasted. The amount of energy wasted in this way will determine how efficiently the device or circuit is operating.

When current flows through a circuit component with a resistance R, energy is consumed or dissipated by that resistance and the component becomes warm. If the current flows for time t and creates a voltage drop V across R, the energy U consumed or dissipated can be calculated using the following formula:

U  =  V  ×  I  ×  t  joules

We can use Ohm's law to derive various formula to express the instantaneous power (in watts) delivered to a circuit component as follows:

P  =  V  ×  I

or

P  =  I 2  ×  R

or

 P  = V 2 R

In alternating current (a.c.) circuits, the same calculations can be used to determine the instantaneous power being delivered to a component, but the voltage and current will be constantly changing. In addition, the a.c. circuit is not purely resistive since it will have circuit elements such as inductors and capacitors that will introduce reactance (opposition to the flow of a.c. current) that will vary in accordance with the phase of the a.c. waveform. This reactance combines with the resistance of the circuit or circuit component to produce impedance. Only the net transfer of energy in one direction (known as real power or active power) can be used to perform work. The remaining energy is returned to its source at the end of each cycle, and is known as reactive power. The subject of power in a.c. circuits is dealt with in more detail elsewhere.

## Problems

1. If a 3 Ω resistor (R1) and a 5 Ω resistor (R2) are placed in series with a 10 V supply, what is the power dissipated in each resistor?

2. What is the power dissipated in each resistor if they are connected in parallel with the supply?