# Energy and Power Efficiency Formulas in Electrical Engineering

Energy is available in numerous forms from different natural sources such as hydro energy from pressure heads of water, nuclear energy from fuels like uranium, the chemical energy of fuels, wind energy, etc. Using suitable methods and by installing power plants different forms of energy can be converted into electrical energy.

During the conversion process, some energy is always lost. As a result of this, the output energy is always less than the input energy.

Energy efficiency is defined as the output energy divided by the input energy.

Efficiency = Output energy/Input energy

Just like energy, power efficiency is defined as the output power divider by the input power.

Efficiency = Output power/Input power

Lowercase Greek Alphabet Letter Eta is used to represent efficiency (η)

In the case of practical real-life systems, the value of efficiency is always less than 1. In terms of percentage, it is always less than 100%.

Let’s solve some examples to understand this

Example 1:

If input energy is 100 kWh, and output energy is 90 kWh. Compute the efficiency of the system.

Solution: Efficiency = 90 kWh/100 kWh = 0.9 = 90%

Example 2:

Certain system takes 50 W input power while producing 40 W output power. Calculate the efficiency of the system.

Solution: Efficiency = 40 W/50 W = 0.8 = 80%

Example 3:

A prime mover supplies mechanical energy to a DC generator at the rate of 2000 J/s. The generator delivers 10 A at 120 V. Calculate the percentage efficiency of the generator.

Solution:

Input power P(i) = 2000 J/s

Output power P(o) = VI = 10 * 120 = 1200 W

Efficiency = 1200/2000 = 0.6 = 60%