Curious, as you'll find me to be..
When you state 'R' are you speaking of resistance of the motor?
And would you explain that more?
P = E^2 / R
Sorry so long getting back to you. I haven't been on the board for a while.
This was a calculation for a dump load resistor, seeking to calculate the
normal-operating-temperature resistance of an electric heating element
from its power (P in watts) and voltage (E in RMS Volts) rating.
(The comments about calculators inspired me to run it thorugh in
a form that could be easily done by hand.)
P = E ^ 2 / R is "Power = Voltage Squared divided by Resistance."
This comes form combining
Ohm's Law (E = I * R, where I is current in amps) with the
formula for electrical power (P = E * I where P is power in watts).
I used ^ for the "exponentiation" operator, as is done in some
computer languages, rather than trying to get a superscript-2
into the text.
With this you should be able to understand and check the
computations yourself.
The idea was to estimate the resistance from the power rating
of a 120-volt heating element, in order to select one that would
provide the desired dump load if 70 volts was applied. That
comes out to about a 300 watt heating
element IF the resistance didn't change with temperature.
Since resistance of heating element wire does go up as it
get hotter, a 300 watt heater operating at 70 volts would
actually more current than intended, so I ballparked the
correction by going to the next lower typical value.