Harold Hall

The resulting value can be calculated using the formula.


     Rt  =  ———————————

              1     1

             ——— + ———

              R1    R2


For more than two resistors the formula simply expands as follows.



 Rt  =  —————————————————

          1     1     1

         ——— + ——— + ———

          R1    R2    R3


The resulting overall resistance, Rt, for the circuit in Sk 6 is arrived at by considering it in two stages. First, two resistors, R2 and R3, in parallel as in Sk 5 and summing this value with the R1, as in Sk 4.


Placing two resistors in series will be for one of two reasons. 1, if the value required is not available and has to be arrived at using two of lower value, not necessarily the same. Or 2, and more likely, to tap off a smaller voltage than that applied to the circuit as illustrated by Sk 7.


In this case the ratio of resistor values R2 : R1 + R2 will be identical to the ratio of the output to input voltages.



Workshop Data


Basic Circuits

The most basic of circuits is were a voltage (V) is feeding a resistor (R) resulting in a current (I), Sk3.

In this case the current (I) is dependent on the values of V and R. Current will increase proportionally with voltage and inversely proportional with resistance. That is, typically, twice the voltage resulting in twice the current but twice the resistance resulting in half the current. The formula for this basic circuit  is


            I = ——— amps



Before we expand on that simple circuit it is necessary to understand the result of using multiple resistors. This can be with them in series (Sk 4), parallel (Sk 5) or complex circuits (Sk 6).

The total resistance, Rt, when connecting two resistors in series is the sum of the two values. The formula being.


                Rt = R1 + R2


Placing two resistors in parallel is more complex but the resulting value will always be smaller than that of the smallest. Typically, with high and low value resistors in parallel the result will be a little less than that of the lower value.


Vo  =  Vin  x   —————————

                R1 + R2


This though is an over simplification as the output voltage, Vo, will be feeding a load that will have its own resistance value. The circuit Sk 6 is therefore more appropriate where R3 is the load.

In this case the value of R2 and R3 in parallel should be used in the ratio. I suspect that some viewers will consider that I am discussing electronic circuits and whilst my comments could be applicable to these they are equally at home in non electronic systems.