.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrical_engineering/dc_circuits/plot_03_kirchhoff_nodal_analysis.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_electrical_engineering_dc_circuits_plot_03_kirchhoff_nodal_analysis.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_electrical_engineering_dc_circuits_plot_03_kirchhoff_nodal_analysis.py:


Kirchhoff's circuit laws and nodal analysis (1845)
==================================================

In 1845, as a student in Königsberg, Gustav Kirchhoff stated the two laws
that make any network of conductors solvable: the currents meeting at a
junction sum to zero, and the voltages around any closed loop sum to zero.
Writing the current law at every node, with Ohm's law for each branch,
gives a linear system :math:`G\mathbf{v} = \mathbf{i}`, nodal analysis.
Circuit simulators add one row per voltage source, *modified* nodal
analysis (:func:`~engineeringkit.electrical_engineering.nodal_analysis`).
This example solves a two-source ladder network, checks both of
Kirchhoff's laws on the result, and verifies superposition.

.. GENERATED FROM PYTHON SOURCE LINES 17-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.electrical_engineering import nodal_analysis








.. GENERATED FROM PYTHON SOURCE LINES 23-28

A ladder with two sources
-------------------------

A 12 V source at node 1 and a 2 mA current source into node 4 drive a
resistor ladder. Node 0 is ground.

.. GENERATED FROM PYTHON SOURCE LINES 28-36

.. code-block:: Python


    resistors = [(1, 2, 1e3), (2, 0, 2e3), (2, 3, 1e3), (3, 0, 2e3), (3, 4, 1e3), (4, 0, 2e3)]
    vsrc, isrc = [(1, 0, 12.0)], [(0, 4, 2e-3)]
    result = nodal_analysis(4, resistors, current_sources=isrc, voltage_sources=vsrc)
    for k, v in enumerate(result.voltages):
        print(f"node {k}: {v:7.4f} V")
    print(f"source current {result.source_currents[0] * 1e3:.3f} mA, KCL residual {result.kcl_residual:.1e} A")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    node 0:  0.0000 V
    node 1: 12.0000 V
    node 2:  6.5116 V
    node 3:  4.2791 V
    node 4:  4.1860 V
    source current 5.488 mA, KCL residual 9.4e-19 A




.. GENERATED FROM PYTHON SOURCE LINES 37-42

Both laws hold
--------------

The current law is the solver's residual. The voltage law holds around
the loop 0-1-2-0: the source rise equals the two resistor drops.

.. GENERATED FROM PYTHON SOURCE LINES 42-62

.. code-block:: Python


    v = result.voltages
    i = result.resistor_currents
    assert result.kcl_residual < 1e-15
    assert np.isclose(12.0, i[0] * 1e3 + i[1] * 2e3)

    # Superposition: each source alone, the other zeroed.
    only_v = nodal_analysis(4, resistors, voltage_sources=vsrc)
    only_i = nodal_analysis(4, resistors, current_sources=isrc, voltage_sources=[(1, 0, 0.0)])
    assert np.allclose(v, only_v.voltages + only_i.voltages)

    fig, ax = plt.subplots()
    x = np.arange(v.size)
    ax.bar(x - 0.25, only_v.voltages, 0.25, label="12 V source alone")
    ax.bar(x, only_i.voltages, 0.25, label="2 mA source alone")
    ax.bar(x + 0.25, v, 0.25, label="both")
    ax.set(xlabel="node", ylabel="voltage [V]", title="Nodal analysis and superposition")
    ax.legend()

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/dc_circuits/images/sphx_glr_plot_03_kirchhoff_nodal_analysis_001.png
   :alt: Nodal analysis and superposition
   :srcset: /api/gallery/electrical_engineering/dc_circuits/images/sphx_glr_plot_03_kirchhoff_nodal_analysis_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.027 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_dc_circuits_plot_03_kirchhoff_nodal_analysis.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/electrical_engineering/dc_circuits/plot_03_kirchhoff_nodal_analysis.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_kirchhoff_nodal_analysis.ipynb <plot_03_kirchhoff_nodal_analysis.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_kirchhoff_nodal_analysis.py <plot_03_kirchhoff_nodal_analysis.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_kirchhoff_nodal_analysis.zip <plot_03_kirchhoff_nodal_analysis.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_