Thevenin Equivalent Circuit Reducer

Physics Electricity and Magnetism • Current and Circuits

Written by STEM Calculators Team Published January 14, 2026 Updated February 24, 2026

9. Thevenin Equivalent Circuit Reducer

Reduce a circuit seen at terminals a–b to its Thevenin form: $V_{\mathrm{th}}$ in series with $R_{\mathrm{th}}$ . Optionally analyze a load $$R_L$$ and preview how $$V_L$$ , $$I_L$$ , or $$P_L$$ change as $$R_L$$ varies.

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication.

Circuit + Inputs

Original circuit model: Battery voltage $V_s$ (V): Resistor $R_1$ (Ω): Resistor $R_2$ (Ω): Current source $I_s$ (A): Open-circuit voltage $V_{oc}$ (V): Short-circuit current $I_{sc}$ (A): Load $R_L$ (Ω): Include load analysis: Plot $V_L/I_L/P_L$ vs $R_L$: Plot variable: Plot max $R_L$ (Ω): Cursor fraction $f\in[0,1]$ (dot): Schematic diagram: Play speed (moves dot):

The slider $f$ only moves the dot on the plot along the chosen $R_L$ range for visualization. It does not change your entered load value.

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Steps

Enter values and click Solve.

Schematic: original vs Thevenin equivalent

Clean schematic (labels won’t overlap)

Load sweep preview

Plot with pan/zoom

Hover: (R_L, y)=…

Drag to pan. Use mouse wheel / trackpad to zoom. Double-click to reset.

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Theory — 9. Thevenin Equivalent Circuit Reducer

Thevenin’s theorem says that any linear two-terminal circuit made of sources and resistors can be replaced (as seen from the terminals) by a single voltage source $V_{\text{th}}$ in series with a single resistance $R_{\text{th}}$. This is extremely useful for quick load analysis and maximum power transfer.

1) The Thevenin model

\[ \text{Original network at terminals }(a,b)\quad\Longleftrightarrow\quad \boxed{V_{\text{th}} \text{ in series with } R_{\text{th}}}. \] \[ I_L=\frac{V_{\text{th}}}{R_{\text{th}}+R_L},\qquad V_L=I_LR_L,\qquad P_L=I_L^2R_L. \]

2) How to find $V_{\text{th}}$ and $R_{\text{th}}$

The calculator emphasizes the open-circuit / short-circuit method:

\[ V_{\text{th}} = V_{\text{oc}} \quad\text{(open-circuit voltage at the terminals)} \] \[ I_{\text{sc}} \quad\text{(short-circuit current when the terminals are shorted)} \] \[ R_{\text{th}}=\frac{V_{\text{th}}}{I_{\text{sc}}}. \]

An alternative (not required here) is to deactivate independent sources and compute the equivalent resistance seen at the terminals: ideal voltage sources $\rightarrow$ short, ideal current sources $\rightarrow$ open.

3) Preset example: voltage divider

For a voltage source $V_s$ with $R_1$ and $R_2$ in series and the output taken across $R_2$, the Thevenin values are:

\[ V_{\text{th}} = V_s\frac{R_2}{R_1+R_2},\qquad R_{\text{th}} = R_1\parallel R_2=\frac{R_1R_2}{R_1+R_2}. \]

4) Norton dual

The Norton equivalent is a current source $I_N$ in parallel with $R_N$, where:

\[ I_N=\frac{V_{\text{th}}}{R_{\text{th}}},\qquad R_N=R_{\text{th}}. \]

5) Maximum power transfer

For a purely resistive load, the load power is maximized when:

\[ R_L = R_{\text{th}}. \]

This is why the graph shows a dashed marker at $R_L=R_{\text{th}}$.

Note: Thevenin/Norton equivalence assumes linear elements. Nonlinear devices (diodes, transistors in nonlinear regions, etc.) require small-signal linearization or different methods.

Steps

Schematic: original vs Thevenin equivalent

Load sweep preview

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