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2.3: Parallel Circuits

  • Page ID
    3268
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    • Contributed by Camosun College
    • Sourced from BCCampus (Download for free at http://open.bccampus.ca/find-open-textbooks)

    The parallel circuit (Figure \(\PageIndex{1}\)) has completely different characteristics. In a parallel circuit, two or more loads are connected side by side and are controlled by one or more switches. The different loads can each have their own switch, but the major difference is that each of the loads has access to the same amount of voltage and can operate independently of the others. There is more than one path through which the current can flow.

    parallelCircuit.png
    Figure \(\PageIndex{1}\): Parallel circuit (CC BY-NC-SA; BC Industry Training Authority)

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    parallelCircuit2.png
    Figure \(\PageIndex{2}\): Parallel circuit (CC BY-NC-SA; BC Industry Training Authority)

    \[\begin{array}{l}{\mathrm{I}_{1}=\frac{\mathrm{E}_{1}}{\mathrm{R}_{1}}=\frac{120}{40}=3 \mathrm{amps}} \\ {\mathrm{I}_{2}=\frac{\mathrm{E}_{2}}{\mathrm{R}_{2}}=\frac{120}{10}=12 \mathrm{amps}} \\ {\mathrm{I}_{3}=\frac{\mathrm{E}_{3}}{\mathrm{R}_{3}}=\frac{120}{240}=0.5 \mathrm{amp}}\end{array}\]

    \[R_{T}=\frac{E_{T}}{I_{T}}=\frac{120}{15.5}=7.7 \text { ohms }\]

    \[R_{T}=\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \ldots}\]

    \[\begin{aligned} R_{T}=& \frac{1}{\frac{1}{40}+\frac{1}{10}+\frac{1}{240}}=7.7 \text { ohms } \\ R_{T}=& \frac{1}{\frac{6}{240}+\frac{24}{240}+\frac{1}{240}} \\ R_{T}=& \frac{\frac{240}{240}}{31} \\ R_{T}=& 7.7 \text { ohms } \end{aligned}\]

    1.png
    Figure \(\PageIndex{3}\): Parallel circuit with four resistors (CC BY-NC-SA; BC Industry Training Authority)
    2.png
    Figure \(\PageIndex{4}\): Parallel circuit with two resistors (CC BY-NC-SA; BC Industry Training Authority)