Shorts cuts for fun

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ronaldrc

Senior Member
Location
Tennessee
Math short cuts I have found to make electrical calculations simple.

Short cut #1

I always had a problem dividing long numbers but not multiplying them so I come up
with this.

Example What is the load capacity of a 75 KW single phase transformer at 240 volts?

Conventional way divide----75000 / 240=312 amps.

My way is to multiply by the reciprocal of the voltage in this case is 240 volts.

The reciprocal of 240 is .0041666

Example .0041666 x 75000=312 amps.


You can find the reciprocal of a number by dividing 1 by the number.

Example 1 divide by 120 volts, 1 / 120=.083333

You can make a list of the logarithms of these numbers.

1.-120=.00833
2.-240=.00416
3.-277=.00361
4.-480=.00208


Short cut #2

If an electrical heater dissipates 2000 watts at 208 volts what would this same heater
dissipate at 240 volts. This is assuming the heaters resistance does not increase or
decrease with the extra 32 volts.

Conventional way first find the amperes of the heater. 2000 / 208=9.6 amps.

Next find the resistance in ohms of the heater. 208 / 9.6=21.6 ohms

Next find how many amperes the heater will pull at 240 volts 240/21.66=11.11 amps.

Next and last we can multiply to find watts at 240 volts 11.11 x 240=2666 watts

My way is one step multiply 2000 x 1.333=2666 watts

You can use 1.33313609 with the wattage ratio between 208 and 240 only.

Here is a table of ratios
120 to 130=1.1726 or for practical use 1.17
208 to 240=1.33313609 ? ? ? ? 1.33
240 to 277=1.3321006 ? ? ? ? 1.332

You can also reverse this process by dividing.

Example a 120 volt, 100 watt light bulb dissapates aprox. 85 watts at 130 volt.

100 / 1.17=85 watts or 85.28 watts


Ronald :)
 
Re: Shorts cuts for fun

Well, for your fist example, you're still doing a difficult division to get your reciprocal! It's all just the same if you're using a calculator.

The second one is approaching the equation from a different direction, I do it all the time. :p
 
Re: Shorts cuts for fun

Sam you can make a list of the numbers to multiply with but like you say with a $1.00 calculator who needs it, maybe just something different to talk about. :p :p
 
Re: Shorts cuts for fun

You guys aren't old enough to remember the cost of the first handheld calculators--around $400 in 1970. In 1950, a Remington 99 printing calculator, (mechanical), went for $600. Gasoline was about 22 cents per then, so at $2.20 now, that is not so bad.
 
Re: Shorts cuts for fun

Well Rattus, you might not be old enough to remember my first "mechanical" calculator!
Large_wooden_abacus.jpg
That was before we had gasoline.
 
Re: Shorts cuts for fun

Sam, you were lucky enough to have the large read out model. ;)

Roger
 
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