I try and rely on mental estimations for figuring ohms law stuff but I am having trouble finding some rules to calculate these things in my head, especially when there are Milli-amps or Micro-amps and Mega-ohms and Kilo-Ohms. So if I have a problem like

12 Volts
3microamps

And I want ohms I know it is going to be 4 something but is there a simple rule I can follow to figure how many decimal places over?

Same with things like

12 uV
3M

I know that the above is really

12^-6
3^6

and that they cancel but it gets tricky when it is .120uV and 30M and the decimal moves around.



Those of you who do there in their heads real fast are there some general shortcuts you follow? Do you convert them all over to Volts, ohms and milliamps first? When things get real big or small how are you sure you have the right number of zeros? I can figure it out on paper and with a calculator but I am trying to develop a more rapid way of figuring things out with estimation just using my head. Yes, I do know how to do this with a calculator.

 

You are really comparing three separate methods of calculation:

1) mentally
2) paper and pencil
3) calculator

There are solid reasons for abandoning the calculator. Both methods 1) and 3) are prone to errors. I prefer to use pencil and paper.

I do not always convert to scientific notation, i.e. 1M = 10^6 and 1μ = 10^-6.

Remember that 1/1M = 1μ

Hence 12V/3μA = 4MΩ

12μV/3MΩ = 4pA (the units do not cancel)

0.12μV/3MΩ = 0.04pA

0.12mV/3MΩ = 120μV/3MΩ = 40pA

Also, look for ways of simplifying the denominator

1.2μV/2.5kΩ = 4.8 x 10^-6 / 10 x 10^3 = 0.48nA

0.12μV/330kΩ = 0.36μV/990kΩ ≈ 0.36pA

 

........................
So if I have a problem like

12 Volts
3microamps

The way I do it is just move the denominator prefix to the numerator by inverting its value. Thus micro on the bottom becomes Meg on the top and vice-versa so 12V/3μA = 4 megohms.

....................but it gets tricky when it is .120uV and 30M and the decimal moves around.

Here meg on the bottom gives micro on the top or (.120 micro * micro V / 30Ω) = (120milli * pico V /30Ω) = (40milli picoamps) or .04pA.

Of course for this to work mentally, you need to know the inversion values for all the prefixes:

10^-3 milli \(\leftrightarrow\) kilo 10^3
10^-6 micro \(\leftrightarrow\) mega 10^6
10^-9 nano \(\leftrightarrow\) giga 10^9
10^-12 pico \(\leftrightarrow\) tera 10^12
10^15 femto \(\leftrightarrow\) peta 10^15

 

but it gets tricky when it is .120uV and 30M and the decimal moves around.

I'd first convert the values into a N.Mx10^y format:

.120μV = .12x10^-6 = 1.2x10^-7
30MΩ = 30x10^6 = 3.0x10^7

So 1.2x10^-7 / 3.0x10^7 = (1.2/3.0)x10^(-7-7) = 0.4x10^-14 = 4x10^-15.