Series And Parallel Combination

Resistor networks are reduced by treating parallel branches, where the reciprocal of the equivalent resistance equals the sum of reciprocals, and series elements, where resistances simply add. First the parallel pair is combined: (\frac{1}{R_p} = \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6}), giving (R_p = 2;\Omega). This equivalent then sits in series with the 4 (\Omega) resistor, so the total is (R = R_p + 4 = 2 + 4 = 6;\Omega). The value 13 (\Omega) is wrong because it adds all three resistors as if entirely in series. The value 2 (\Omega) ignores the series resistor and reports only the parallel section. The value 9 (\Omega) wrongly takes the parallel pair as 5 (\Omega). This applies the NCERT rules for combining resistors in mixed networks. A plausibility check confirms the result, since the parallel equivalent must be smaller than the smallest branch (less than 3 (\Omega)), and adding 4 (\Omega) in series sensibly raises the total to 6 (\Omega). Conceptually, the parallel section offers the charge two alternative routes and so lowers the opposition, whereas the series resistor lies on the single common path that every electron must traverse, which is why the two combination rules differ in form yet are applied sequentially to collapse the whole network into one equivalent value.