# Efficiency

Any motor or similar device that converts energy from one form to another can be represented by a "black box" with an energy input and output terminal.

The conservation of energy states that:

Power input = Power output + lost energy or stored inside the black box.

By dividing the two sides of the ratio t is.

Since P = W / t, we have the following:

P_{i }= P_{0} + P _{Lost or stored}

_{Th}_{e efficiency}_{ (Ƞ) of the device to the bottom of the black box is given by the following equation:}

and

When expressed as a percentage, we have:

In terms of energy input and output, efficiency, in percent, is given by

Example 1. A motor of 2 hp operates with an efficiency of 75%. What is the power input in watts? If the input current is 9.05 amperes, what is the input voltage?

Solution:

and

Example 2 . What is the horsepower output of an engine with an efficiency of 80 % and an input current 8 amps at 120 v ?

Solution:

Example 3 . What is the efficiency percentage of a system in which the input energy is 50 joules output and 42.5 joules ?

Solution:

The basic components of a generator (FEM ) are presented in Figure 1 . The mechanical power source is similar to a paddle wheel which rotates due to the water falling from the weir structure . Then the gear train ensures that the rotating member of the generator set speed turn.

Figure 1 . Basic components of a generator system.

Then , the output voltage must be fed to the load , through a transmission system . Indicated power input and one output for each system component. The efficiency of each system is given by :

If we form the product of these three efficiencies,

and substitute that Pi2 = P01 = P02 and PI3 discover that the amounts shown are canceled , we resulting P03 / Pi1 , which is a measure of the efficiency of the entire system .

In general , for the cascade system shown in Figure 2.

Ƞ*Total*_{ = Ƞ1 . Ƞ2 . Ƞ3 , ....................., ȠȠ }

Figure 2 . Cascade system .

Determine the overall efficiency of the system of Figure 1 if Ƞ 1 = 90 % , 2 = 85 % Ƞ , Ƞ 3 = 95 % .

Solution:

Ƞ_{T}_{ = }Ƞ_{1 }Ƞ_{2 }Ƞ_{3 }_{=}_{ }_{(0.90) (0.85) (0.95) = 0.75}_{ O }_{75%}

If one Ƞ efficiency decreases to 60 % , dermínese new efficiency and compare the result with that obtained .

Solution:

Ƞ_{T}_{ = }Ƞ_{1 }Ƞ_{2 }Ƞ_{3 }_{=}_{ }_{(0.60) (0.85) (0.95)}_{ }_{= 0.485 O 48.5%}

Indeed , 48.5 % is significantly lower than 75 %, therefore , the overall efficiency of a cascade system is determined primarily by the lower efficiency ( the weakest link ) and is lower ( or equal if the remaining efficiencies are 100% ) that the link in the system less efficient .

Font : Robert L. Boylestad, Análisis introductorio de circuitos, Pág. 80-83.