October 1958 RadioElectronics
[Table
of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioElectronics,
published 19301988. All copyrights hereby acknowledged.

If you have ever placed
a fixed resistor in parallel with a potentiometer to reduce the total resistance,
then you are familiar with how you also convert a linear relationship of the wiper
movement with resistance to one that is nonlinear. That is because the equation
changes from R_{total} = R_{x:potentiometer} (where x
is the potentiometer position) to R_{total} = (R_{x:potentiometer} * R_{parallel}) / (R_{x:potentiometer} +
R_{parallel}). The graph of it looks like one of the curves in this chart.
Since the total parallel resistance is always smaller than the lowest value of the
two resistances, the greater the ratio of the two is, the more dominant the smaller
resistance value becomes. That means as the potentiometer wiper approaches the minimum
resistance end of its travel, the parallel resistor attached across it has virtually
no effect.
Since parallelconnected inductors and seriesconnected capacitors scale in the
same manner as parallelconnected resistors, this chart is useful for those circuits
as well. Seriesconnected resistors and inductors, and parallelconnected capacitors
are simply the sums of their individual values. Consequently, if you connect a fixed
resistor in series with a potentiometer, the total resistance at any position of
the potentiometer wiper will be the linear sum of the fixed resistor and the potentiometer
resistance. Got that?
* Theoretically, x is a value from 0 to 1 that represents the relative position
of the potentiometer wiper contact.
Parallel Resistance Chart
By Rudolph Wellsand
To use the chart locate R_{1} along the top scale and R_{2} on
the lefthand scale. Find the point where they meet on a curve. Trace the curve
to the R_{T} scale and read the answer. For total values of parallel inductance
and series capacitance use the scales at the bottom and right hand edges. To extend
the ranges of the scales, either multiply or divide each value in every scale by
1,000.
Posted June 9, 2022 (updated from original post on 1/4/2015)
