Efficiency is one of the most frequently used words in physics, engineering, economics, and life. Efficiency tells us how efficient something is at using resources to produce a result.

What is Efficiency?

In simple terms, efficiency is the ratio of how effectively the system input is converted into output. Normally, it is given as a percentage measure of how much of the input gets successfully transformed into the desired output.

Formula 

On the basis of useful output to total input, efficiency can be estimated numerically. The ratio of energy transferred to useful form with the total energy supplied at the initial stage is called the efficiency of the device.

η denotes Efficiency.

Efficiency formula in relation to Work is expressed as,

The Energy efficiency formula is,

The efficiency formula is used to calculate the efficiency of any given input. It has no unit and is expressed in percentage.

Solved Problems

Problem 1: A cyclist does 600 J of work on his bicycle and the bicycle produces only 140 J of useful work. Determine the efficiency of a cyclist.

Solution:

Given,

Work Input = 600 J,

Work Output = 140 J

The efficiency is given as

η ={ Work Output / Work Input }× 100 %

 = {140 / 600} × 100 %

= 23.3 %

Problem 2: A heat engine performs 500 J of useful work. Calculate the energy supplied to it as input if its efficiency is 40%.

Solution:

Given,

Energy output = 500 J

Efficiency η = 40 %

The formula is given as,

∴ Energy input = Energy Output / η

                        = 500 / 0.40

                        = 1250 J

 

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