.. 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_02_wheatstone_bridge.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_02_wheatstone_bridge.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_02_wheatstone_bridge.py:


Wheatstone's bridge (1843)
==========================

Samuel Hunter Christie described the circuit in 1833, and Charles
Wheatstone made it the standard way to measure resistance in his 1843
Bakerian lecture. Two voltage dividers share a source; a galvanometer joins
their midpoints. When :math:`R_1/R_2 = R_3/R_4` the midpoints sit at the same
potential and the galvanometer reads zero, whatever the source voltage
(:func:`~engineeringkit.electrical_engineering.wheatstone_balanced`). A null
reading needs no calibrated meter, which is why the bridge is so accurate.
This example balances a bridge against an unknown resistor and shows how
sharply the null depends on it.

.. 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, wheatstone_balanced








.. GENERATED FROM PYTHON SOURCE LINES 23-28

The galvanometer current
------------------------

Nodes: 1 the source, 2 and 3 the midpoints. The unknown :math:`R_x` is
:math:`R_4`; :math:`R_3` is the calibrated adjustable arm.

.. GENERATED FROM PYTHON SOURCE LINES 28-43

.. code-block:: Python


    R1, R2, Rx, Rg, V = 1000.0, 1000.0, 472.0, 50.0, 5.0


    def galvanometer_current(R3):
        bridge = [(1, 2, R1), (2, 0, R2), (1, 3, R3), (3, 0, Rx), (2, 3, Rg)]
        return nodal_analysis(3, bridge, voltage_sources=[(1, 0, V)]).resistor_currents[4]


    R3 = np.linspace(400, 550, 301)
    ig = np.array([galvanometer_current(r) for r in R3])
    balance = R3[np.argmin(np.abs(ig))]
    print(f"null at R3 = {balance:.1f} ohm, so Rx = R3 R2 / R1 = {balance * R2 / R1:.1f} ohm")
    assert wheatstone_balanced(R1, R2, balance, Rx)





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

 .. code-block:: none

    null at R3 = 472.0 ohm, so Rx = R3 R2 / R1 = 472.0 ohm




.. GENERATED FROM PYTHON SOURCE LINES 44-46

The null does not depend on the source
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 46-60

.. code-block:: Python


    for v_source in (1.0, 5.0, 20.0):
        bridge = [(1, 2, R1), (2, 0, R2), (1, 3, Rx), (3, 0, Rx), (2, 3, Rg)]
        i_null = nodal_analysis(3, bridge, voltage_sources=[(1, 0, v_source)]).resistor_currents[4]
        assert abs(i_null) < 1e-15

    fig, ax = plt.subplots()
    ax.plot(R3, ig * 1e6)
    ax.axhline(0, color="gray", lw=0.5)
    ax.axvline(Rx, color="C3", ls="--", label="$R_3 = R_x R_1/R_2$")
    ax.set(xlabel="adjustable arm $R_3$ [ohm]", ylabel="galvanometer current [µA]", title="Balancing a Wheatstone bridge")
    ax.legend()

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/dc_circuits/images/sphx_glr_plot_02_wheatstone_bridge_001.png
   :alt: Balancing a Wheatstone bridge
   :srcset: /api/gallery/electrical_engineering/dc_circuits/images/sphx_glr_plot_02_wheatstone_bridge_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.035 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_dc_circuits_plot_02_wheatstone_bridge.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_02_wheatstone_bridge.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_wheatstone_bridge.ipynb <plot_02_wheatstone_bridge.ipynb>`

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

      :download:`Download Python source code: plot_02_wheatstone_bridge.py <plot_02_wheatstone_bridge.py>`

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

      :download:`Download zipped: plot_02_wheatstone_bridge.zip <plot_02_wheatstone_bridge.zip>`


.. only:: html

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

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