Question

Why do two or more resistors connected in series and parallel have different effective resistances?

Answer 1

In a series connection, the same current flows through every resistor and the total potential difference is the sum of the individual potential differences. Hence, the effective resistance is the sum: \[R_{\mathrm{s}}=R_{1}+R_{2}+R_{3}+\cdots\]. It is therefore greater than any individual resistance. In a parallel connection, the same potential difference acts across every resistor, while the total current divides among the branches. Thus, conductances add: \[\frac{1}{R_{\mathrm{p}}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\cdots\]. Therefore, the effective resistance in parallel is less than the smallest individual resistance. Series connections provide one path for current, whereas parallel connections provide multiple paths.