Here we have two resistances of 3 ohms and 6 ohms which are connected in parallel. This arrangement is shown in Figure given below. Now, we want to find out their equivalent resistance or resultant resistance. We know that when two resistance `R_(1)` and `R_(2)` are connected in parallel, then their equivalent resistance R is given by:
`(1)/(R) = (1)/(R_(1))+(1)/(R_(2))`
Here, `r_(1) = 3` ohms
and, `R_(2) = 6` ohms
So, `(1)/(R) = (1)/(3)+(1)/(6)`
or `(1)/(R) = (2+1)/(6)`
or `(1)/(R) = (3)/(6)`
or `(1)/(R) = (1)/(2)`
and `R = 2 Omega`
Thus, the equivalent resistance is 2 ohms.
So far we have studied the combination of resistances in series and parallel separately. Many times, however, the practical electrical circuits involve the combination of resistances in series as well as in parallel in the same circuit. We will now solve a problem in which the resistance are connected in series as well as in parallel in the same circuit.