Question

Let there be n resistors R₁ . ..........R_n with R_max = max (R₁......... R_n) and R_min = min {R₁ ..... R_n}. Show that when they are connected in parallel, the resultant resistance R_P< R_min and when they are connected in series, the resultant resistance R_S > R_max. Interpret the result physically.

Answer 1

and R_S = R₁ + . ..... + R_n ≥ R_max.

In Fig. (b), R_min provides an equivalent route as in Fig. (a) for current. But in addition there are (n – 1) routes by the remaining (n – 1) resistors. Current in Fig.(b) > current in Fig. (a). Effective Resistance in Fig. (b) < R_min. Second circuit evidently affords a greater resistance. You can use Fig. (c) and (d) and prove R_s > R_max.