Consider two resistors connected in *series*, as shown in Fig. 18.
It is clear that the same current flows through both resistors.
For, if this were not the case, charge would build up in one or other
of the resistors, which would not correspond to
a steady-state situation (thus violating
the fundamental assumption of this section). Suppose that the potential drop
from point to point is . This drop is the sum of the potential
drops and across the two resistors and , respectively.
Thus,

(135) |

(136) |

Here, we have made use of the fact that the current is common to all three resistors. Hence, the rule is

For resistors connected in series, Eq. (137) generalizes to .The equivalent resistance of two resistors connected in series is the sum of the individual resistances.

Consider two resistors connected in *parallel*, as shown in Fig. 19. It
is clear, from the figure, that the potential drop across the two resistors is the
same. In general, however, the currents and which flow
through resistors and , respectively, are different.
According to Ohm's law, the equivalent resistance
between and is the ratio of the potential drop
across these points and the current
which flows between them. This current must equal the sum of the
currents and flowing through the two resistors, otherwise
charge would build up at one or both of the junctions in the circuit.
Thus,

(138) |

(139) |

Here, we have made use of the fact that the potential drop is common to all three resistors. Clearly, the rule is

For resistors connected in parallel, Eq. (140) generalizes to .The reciprocal of the equivalent resistance of two resistances connected in parallel is the sum of the reciprocals of the individual resistances.