ABSTRACT
In Eq. (7-91) we used an impedance method which may have been unfamiliar to you, though it may have seemed intuitively correct since you know that parallel resistors combine as R 1 R2/(R 1 + R2). Using Fig. 7-37 we want to develop rules for combining arbitrary impedances (not just resistors) in series and parallel. For the series combination, both Z 1 and Z2 must carry the same current i; thus
Thus the rule for combining impedances in series is to simply add them, just as pure resistances add up in de circuits. Note that this may be done with either operational, Z(D), sinusoidal, Z(iw), or Laplace, Z(s), impedances. Applying this method to the circuit of Fig. 7-30a, the impedance "seen" by the voltage source ei is the series combination of R and C:
This agrees with Eq. (7-77), which was obtained directly from Kirchhoff's voltageloop law, a different method. Note that our result, derived for the combination of two series impedances, can immediately be extended to any number of series impedances. How?
