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Combined Series-Parallel Circuits

Representing most real world circuits, these circuits are connected in series as well as in parallel.

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Christmas Lights

Christmas Lights

Credit: Donnie Ray Jones
Source: http://www.flickr.com/photos/donnieray/5275681025/
License: CC BY-NC 3.0

Every year millions of people around the world decorate their homes, businesses and offices with multi-colored lights that welcome the holiday season. Are these lights strung together in parallel or are the strung together in series? Read on to find out.

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Credit: martinak15
Source: http://www.flickr.com/photos/martinaphotography/8265875434/
License: CC BY-NC 3.0

Christmas lights are strung together in a series [Figure2]

Circuits have very basic rules that must be followed. Use the following rules below to determine when components are in series or when they are in parallel.

Components (resistors, capacitors, etc.) in a circuit are either considered to be in series with one another or in parallel, they cannot be in both. Components in series have the following properties:

  • Carry the same current
  • Resistors add as: \begin{align*}R_{equivalent} = \sum \limits_{i} R_i = R_1 + R_2 + \cdots \end{align*}
  • Capacitors add as the reciprocal: \begin{align*}\frac{1}{C_{equivalent}} = \sum \limits_{i} \frac{1}{C_i} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots\end{align*}

Components in parallel have the following properties:

  • The potential drop across all the components is the same
  • Resistors add as: \begin{align*}\frac{1}{R_{equivalent}} = \sum \limits_{i} \frac{1}{R_i} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots\end{align*}
  • Capacitors add as: \begin{align*}C_{equivalent} = \sum \limits_{i} C_i = C_1 + C_2 + \cdots \end{align*}

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Using the information provided above, answer the following questions.

  1. In the string of Christmas tree lights, if one of the lights goes out causing every light to go out, could you say if the lights are in series or parallel?
  2. While sitting in front of the tree one night, you notice that every third light in the string of lights on the tree is unlit. What does this tell you about the circuit?

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Image Attributions

  1. [1]^ Credit: Donnie Ray Jones; Source: http://www.flickr.com/photos/donnieray/5275681025/; License: CC BY-NC 3.0
  2. [2]^ Credit: martinak15; Source: http://www.flickr.com/photos/martinaphotography/8265875434/; License: CC BY-NC 3.0

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