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.


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By dividing the two sides of the ratio t is.



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


Pi = P0 + Lost or stored


The efficiency (Ƞ) of the device to the bottom of the black box is given by the following equation:


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and eficiencia3

When expressed as a percentage, we have:


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

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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?





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



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



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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 :


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If we form the product of these three efficiencies,

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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.

ȠTotal = Ƞ1 .  Ƞ2 . Ƞ3 , ....................., ȠȠ                                  imagen15 articulo3


Figure 2 . Cascade system .

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


ȠT = ȠȠ2 Ƞ= (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 .



ȠT = Ƞ1 Ƞ2   Ƞ= (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.