Electrical Calculations - Basic Mathematics for Water and Wastewater Operators - page 138

-

I = 0.5 A

Light bulb
R = ?

E = 120 V

+

FIGURE 10.8 Ohm's law illustration for Example 10.7.

e leCtriCal p oWer
Power , whether electrical or mechanical, pertains to the rate at which work is being
done, so the power consumption in a plant is related to current flow. A large electric
motor or air dryer consumes more power (and draws more current) in a given length
of time than, for example, an indicating light on a motor controller. Work is done
whenever a force causes motion. If a mechanical force is used to lift or move a weight,
work is done; however, force exerted without causing motion, such as the force of a
compressed spring acting between two fixed objects, does not constitute work.

Note: Power is the rate at which work is done.

e leCtriCal p oWer C alCulations
The electrical power ( P ) used in any part of a circuit is equal to the voltage ( E ) across
that part of the circuit multiplied by the current ( I ) in that part. In equation form:

P = E × I (10.4)

where
P = Power (watts, W).
E = Voltage (volts, V).
I = Current (amps, A).

If we know the current ( I ) and the resistance ( R ) but not the voltage, we can find the
power ( P ) by using Ohm's law for voltage, so by substituting Equation 10.3:

E = I × R

into Equation 10.4, we obtain:

P = ( I × R ) × I = I 2 × R (10.5)

In the same manner, if we know the voltage and the resistance but not the current,
we can find the P by using Ohm's law for current, so by substituting Equation 10.1:

E
R

I =