The networks in parts (a) and (b) of Figure 2.23 show two resistors coupled in series an...

The networks in parts (a) and (b) of Figure 2.23 show two resistors coupled in series and in parallel, respectively. We wish to find a general formula for the effective resistance of each network—that is, find Reff such that E = ReffI.

(a) Show that the effective resistance Reff of a network with two resistors coupled in series [Figure 2.23(a)] is given by Reff = R₁ + R₂

(b) Show that the effective resistance Reff of a network with two resistors coupled in parallel [Figure 2.23(b)] is given by