# Electric power efficiency

### Power efficiency

Power efficiency is defined as the ratio of the output power divided by the input power:

η = 100% ⋅ Pout / Pin

η is the efficiency in percent (%).

Pin is the input power consumption in watts (W).

Pout is the output power or actual work in watts (W).

##### Example

Electric motor has input power consumption of 50 watts.

The motor was activated for 60 seconds and produced work of 2970 joules.

Find the efficiency of the motor.

Solution:

Pin = 50W

E = 2970J

t = 60s

Pout = E / t  = 2970J / 60s = 49.5W

η = 100% * Pout / Pin = 100 * 49.5W / 50W = 99%

### Energy efficiency

Energy efficiency is defined as the ratio of the output energy divided by the input energy:

η = 100% ⋅ Eout / Ein

η is the efficiency in percent (%).

Ein is the input energy consumed in joule (J).

Eout is the output energy or actual work in joule (J).

##### Example

Light bulb has input power consumption of 50 watts.

The light bulb was activated for 60 seconds and produced heat of 2400 joules.

Find the efficiency of the light bulb.

Solution:

Pin = 50W

Eheat = 2400J

t = 60s

Ein = Pin * t = 50W * 60s = 3000J

Since the light bulb should produce light and not heat:

Eout = Ein -Eheat = 3000J - 2400J = 600J

η = 100 * Eout / Ein = 100% * 600J / 3000J = 20%

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