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Parallel Circuit Elements

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Parallel Circuit Elements

Introduction

Circuit elements are said to be connected in parallel if all of the elements share the same pair of nodes. An example of two circuit elements connected in parallel is shown in Fig. 1. Applying KVL around the loop of Fig. 1 results in:

(1)

\[{{\rm{V}}_1} = {{\rm{V}}_2}\]

This result is so common that equation (1) is generally written by inspection for parallel elements such as those shown in Fig. 1 without explicitly writing KVL.

Figure 1. Parallel connection of circuit elements.

Note:

Parallel circuit elements share the same voltage. Elements in parallel can be recognized in two ways:

  • If multiple elements are connected to the same pair of nodes, the elements are in parallel.
  • If applying KVL around a loop results in the conclusion that the voltages in two elements are identical, the elements are in parallel.

Test Your Knowledge!

  1. List which of the elements in the circuit below are in parallel.
  2. List which of the elements in the circuit below are in parallel.
  3. List which of the elements in the circuit below are in parallel.
  4. List which of the elements in the circuit below are in parallel.

Selected Answers:

  1. Elements 2 and 3 are in parallel. Element 4 is in parallel with the 5V source.

  2. None of the elements are in parallel with one another.

  3. Elements 1, 2, and the 2A source are all in parallel with one another. Elements 3 and 4 are also in parallel with one another.

  4. Elements 1 and 8 are in parallel with one another. Elements 6, 7, and the 2A source are all in parallel.

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