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Series Circuit Elements

How to Identify a Series

tag Circuits Series

Series Circuit Elements:

How to Identify a Series

Introduction

Circuit elements are said to be connected in series if all of the elements carry the same current. An example of two circuit elements connected in series is shown in Fig. 1. Applying KCL at node a and taking currents out of the node as positive, we see that:

\[ - {i_1} + {\rm{ }}{i_2} = {\rm{ }}0\] Or \[{i_1} = {\rm{ }}{i_2}\] (1)

Equation (1) is a direct outcome of the fact that the (single) node a in Fig. 1 interconnects only two elements—there are no other elements connected to this node though which current can be diverted. This observation is so apparent (in many cases1) that the equation on the right is generally written by inspection for series elements such as those shown in Fig. 1 without explicitly writing KCL.

Figure 1. Circuit elements connected in series.

Note:

Series circuit elements share the same current. Elements in series can be recognized in two ways:

  • If two and only two elements are connected to a single node, the elements are in series.
  • If applying KCL at a node results in the conclusion that the currents in two elements are identical, the elements are in series.

Test Your Knowledge!

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

Selected Answers:

  1. The 3V source is in series with element 1. Elements 2, 4, and 5 are all in series with each other.

  2. The 9V source is in series with element 1. The 0.5A source is in series with element 4.

  3. None of the elements are in series with each other.

  4. The 4A source, element 1, and element 8 are all in series with each other. The 3V source is in series with element 4. Elements 5 and 7 are in series. Elements 3 and 6 are in series.

  • 1 If there is any doubt whether the elements are in series, apply KCL! Assuming elements are in series, when in actuality they are not, can have disastrous consequences.
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