voltdvdr.tut

--------------

   Voltage Dividers and the Potentiometer: The Voltage Splitting Fraction

    Copyright (c) 1997  Richard Steven Walz - Free For Non-Commercial Use
               All Commercial Rights Reserved By Author


Alright. Let's start at the beginning. You may be aware that two resistors
in series add their resistances to get the sum of resistances for the two
together taken as one. Well, if you connect them to a power source, then
they divide the voltage between them due to each of their resistances, like
so:
                    O V
                    | <----------+
                    /          __|__
                    \  R1     |Volt |   V1 = I * R1  Ohm's Law for R1
                    /         |Meter|   
                    \         |_____|
                    |            |
                    + <----------+
                    |          __|__
                    /         |Volt |   V2 = I * R2  Ohm's Law for R2
                    \  R2     |Meter|
                    /         |_____|
                    \            |
                    | <----------+
                   _|_ Ground         So: V = I * R1 + I * R2  or:
                    -                     V = I * ( R1 + R2 )    
                                          Rtotal = R1 + R2      
 
Now, assuming that no current of appreciable amount flows through the Volt
Meters, and with modern inputs, that's true, the current must flow through
both, and thus be equal in both, as electrons going in are not allowed to
be captured and must come out the other end! Thus I as I have noted is the
same I in both resistances. Then V + I * R , Ohm's Law, MUST also apply to
the two resistances as well as to each singly, and so we now have my few
final equations above stating that the total resistance IS the sum of the
resistances, and that the voltages across each resistance sum to become the
supply voltage V ! Thus, either resistor can be said to be dividing the
voltage between the two resistances off for its share, proportional to its
resistance. The V1 = V - V2 = I * Rtotal - I * R2 = I * ( Rtotal - R2) =
I * ( (R1 + R2) - R2 ) = I * R1 and then they are both also proportional
to their respective R's, and V1 = V * ( R1 / ( R1 + R2 ) ), where the
expression: R1 / ( R1 + R2) is called the "voltage splitting fraction".
And the same goes for more than two resistances, since their Rtotal in
series is the sum of the R's, the denominator is the sum of them all for
more than just two in that fraction.

And so with a potentiometer, which is simply a resistor which can be tapped
at any point along it to divide it effectively into two resistors, the
voltage measured across the tapped portion of it, from either end of
interest, goes as the splitting fraction for that resistance to the end of
interest. See the file on my site ~/TUTS/tranxstr.tut to see what use this
principle of the potentiometer is in dissection of the function of a
bipolar transistor.

Now, if one's quandry is how to use this for a parallel load on one of the
resistances, one must calculate the limits of voltage and current for the
entire network for all varying loads dropped across either of these series
resistances. But the equations are appropriate for tiny currents leaving
the node between resistors, or the wiper-rotor of a potentiometer.

Enjoy!
-Steve
--
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