Skip to main content
Engineering LibreTexts

4.5: Summary

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    In this chapter we have determined how to identify basic series-parallel RLC networks driven by a single effective voltage or current source. The key to this is to identify sub-circuits or subgroups of components that are comprised of either seriesonly or parallel-only configurations within themselves. These groupings can then be reduced to equivalent impedances using the series and parallel combination techniques examined in prior chapters. This process may be repeated until the entire circuit is simplified down to either a single series loop or parallel arrangement of components driven by a voltage or current source.

    Once a circuit has been simplified, series and parallel analysis techniques, and laws such as Ohm's law, Kirchhoff's voltage and current laws, and the voltage and current divider rules, may be employed to determine various voltages and currents in the simplified equivalent. Given these results, the circuit may be expanded back into its original form in stages, reapplying these rules and techniques to determine voltages and currents within the sub-circuits. The process may be iterated until every current and voltage in the original circuit is discovered, if desired.

    As the impedances of the individual sub-circuits can be anywhere between +90 and −90 degrees, phasor diagrams of the various component voltages or currents will no longer exhibit the strict right angles seen in series-only and parallel-only circuits. What is true is that this perpendicular relationship will still exist among the RLC components that comprise a specific series or parallel sub-circuit.

    There are infinite varieties of series-parallel RLC configurations and consequently no single solution technique will work for all of them. In fact, the more complex the circuit, the more solution paths that exist for said circuit. Consequently it is prudent to plan out a solution path instead of just randomly “diving in” as this will lessen the ultimate effort.

    Review Questions

    1. In general, describe the process of reducing an AC series-parallel RLC network down to a single equivalent impedance.

    2. Do Ohm's law, KVL and KCL still apply in AC series-parallel RLC networks? Why?

    3. Is there a finite number of variations of AC series-parallel RLC networks? Why/why not?

    4. Describe a general procedure to find the voltage between two arbitrary points in a series-parallel circuit.

    5. In an AC series-parallel RLC circuit, will it always be the case that voltage across any resistor is in phase with that resistor's current? Why/why not?

    6. In an AC series-parallel RLC circuit, will it always be the case that voltage across any inductor leads any resistor's voltage by 90 degrees? Why/why not?

    This page titled 4.5: Summary is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James M. Fiore via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.