Calculating power using current and voltage

There are three ways of writing an equation for power, current and voltage:

Power = Current × Voltage so

P = I × V or

I = P

V

or

V = P

I

where:

P = power in watts (W) or: P = power in milliwatts (mW)
V = voltage in volts (V)
I = current in amps (A)
V = voltage in volts (V)
I = current in milliamps (mA)

You can use the PIV triangle to help you remember the three versions of the power equations. For most electronic circuits the amper is too large, so we often measure current in milliampers (mA) and power in milliwatts (mW).

1mA = 0.001A and 1mW = 0.001W.

Calculating power using resistance and current or voltage

Using Ohm's Law V = I × R we can convert P = I × V to:

P = I² × R
or
P = V² / R

where:

P = power in watts (W)
I = current in amps (A)
R = resistance in ohms (Ω)
V = voltage in volts (V)

Wasted power and overheating

Normally electric power is useful, making, for example, a lamp light or a motor turn. However, electrical energy is converted to heat when a current flows through a resistance. This can be a problem if a device or wires overheat. In electronics the effect is usually negligible, but if the resistance is low (a wire or low value resistor for example) the current can be very large and can cause a problem.

You can see from the equation P = I² × R that for a given resistance the power depends on the current squared, so doubling the current will give 4 times the power.

Resistors are rated by the maximum power they can pass without damage. Resistors with standard power ratings of 0.25W or 0.5W are suitable for most circuits.

Wires and cables are rated by the maximum current they can pass without overheating. They have a very low resistance so the maximum current is relatively large.

Energy

What is energy? The answer is - energy is the ability to do work.

Energy can be found in a number of different forms. It can be chemical energy, electrical energy, heat (thermal energy), light (radiant energy), mechanical energy, and nuclear energy.

The amount of energy used (or supplied) depends on the power and the time for which it is used:

Energy = Power × Time

A low power device operating for a long time can use more energy than a high power device operating for a short time. For example:

· A 60W lamp switched on for 8 hours uses 60W × 8 × 3600s = 1728kJ.

· A 3kW kettle switched on for 5 minutes uses 3000W × 5 × 60s = 900kJ.

The standard unit for energy is the joule (J), but 1J is a very small amount of energy for mains electricity so units kilojoule (kJ) or megajoule (MJ) are sometimes used in scientific work.

At home we measure electrical energy in kilowatt-hours (kWh). 1kWh is the energy used by a 1kW power appliance when it is switched on for 1 hour:

1kWh = 1kW × 1 hour = 1000W × 3600s = 3.6MJ

For example:

· A 60W lamp switched on for 8 hours uses 0.06kW × 8 = 0.48kWh.

· A 3kW kettle switched on for 5 minutes uses 3kW × ⁵/₆₀ = 0.25kWh.

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