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} = xR_{potentiometer}
(where x is the potentiometer position) to R_{total} = (xR_{potentiometer} • R_{parallel}) / (xR_{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 January 4, 2015
