When there are more than two unequal resistances in parallel the combined resistances can be determined in two ways; first the currents through the individual resistance branches may be found, their sum obtained and this total current divided into the applied voltage,. This will give the total resistance of the parallel combination of the unequal resistances.
The total resistance of unequal parallel resistances can also be determined by the conductance or reciprocal method which is explained in the following paragraphs.
When a definite resistor opposes the flow of current, we say that it has resistance. The same resistor we might say would permit current to flow, that is it has conductance. By definition conductance is the reciprocal of resistance, that is, 1 divided by the resistance. The conductance of a circuit is
Fig. 10
expressed in units called mhos, which is derived from the word ohm written backwards. The symbol for conductance is “G” therefore, “G” = 1 / R.
Now we are ready to fully understand the second method for determining the total resistance of several resistances in parallel.
Suppose we have three resistances in parallel as shown in Fig. 10, having resistances of 2, 5, and 10 ohms respectively. From what we have already said, their respective conductance will be 1/2, 1/5, and 1/15 mho—that is, the total conductance would be equal to G1 + G2 + G3. Since G = 1/R, the total conductance would be
(7)
1 R1
+
1 R2
+
1 R3
Then the total resistance must be equal to the reciprocal of the total conductance, R = 1 / G.
