Simplify Circuits with Thevenin and Norton Theorems

Demonstrative Video

Thevenin’s & Norton’s Equivalent Circuit

  • In a circuit, a particular element is variable (called load) while other elements are fixed

  • If variable element changes, entire circuit needs to be analysed all over again

  • Technique by which the fixed part of the circuit is replaced by an equivalent circuit

  • Used the concept of duality between voltage and current sources

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Thevenin’s Theorem

  • A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a \(V_{th}\) in series with \(R_{th}\)

    • \(V_{th}\) : OC voltage at the terminals

    • \(R_{th}\) : input eq. resistance at the terminals when the independent sources are turned off

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To find \(R_{th}\)

  • Case-1: No dependent source turn off all independent sources and determine \(R_{th}\) at input terminals

  • Case-2: If dependent sources are there turn off only independent sources and then determine \(R_{th}\) by applying 1 V or 1 A at input

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  • The current through and voltage across the load can be easily determined

\[\begin{gathered} I_{L}=\frac{V_{\mathrm{Th}}}{R_{\mathrm{Th}}+R_{L}} \\ V_{L}=R_{L} I_{L}=\frac{R_{L}}{R_{\mathrm{Th}}+R_{L}} V_{\mathrm{Th}} \end{gathered}\]
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Norton’s Theorem

  • A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a \(I_{N}\) in parallel with a \(R_{N}\)

    • \(I_{N}\) : short-circuit current through the terminals and

    • \(R_{N}\) : input equivalent resistance at the terminals when the independent sources are turned off.

    \[\begin{aligned} R_N & = R_{TH} \\ I_{N} & = I_{sc} \\ \Rightarrow I_{N} & = \dfrac{V_{TH}}{R_{TH}} \end{aligned}\]

Measuring \(V_{oc}\) and \(I_{sc}\)

\[\begin{aligned} E_{th} & = V_{oc} \\ I_{sc} & = \dfrac{E_{th}}{R_{th}} \\ R_{th} & = \dfrac{E_{th}}{I_{sc}} \\ \Rightarrow R_{th} & = \dfrac{V_{oc}}{I_{sc}} \end{aligned}\]

Solved Problem

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