.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrical_engineering/transients/plot_02_helmholtz_rl_current.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_transients_plot_02_helmholtz_rl_current.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_transients_plot_02_helmholtz_rl_current.py:


Helmholtz's inductive current rise (1851)
=========================================

When a battery is switched onto a coil, the current does not jump to
Ohm's value: the coil's self-induction opposes the change. Hermann
Helmholtz measured how long induced currents last and in 1851 gave the
law of their rise, :math:`i = (V/R)\left(1 - e^{-Rt/L}\right)`, with the
time scale :math:`L/R`
(:func:`~engineeringkit.electrical_engineering.rl_current`,
:func:`~engineeringkit.electrical_engineering.rl_time_constant`). Opening
the circuit, the current decays with the same time constant. This example
switches a relay coil on and off and checks the energy bookkeeping: what
the source supplies is dissipated in the resistance or stored as
:math:`\tfrac12 L i^2`.

.. GENERATED FROM PYTHON SOURCE LINES 19-25

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.integrate import trapezoid

    from engineeringkit.electrical_engineering import rl_current, rl_time_constant








.. GENERATED FROM PYTHON SOURCE LINES 26-30

Switching on
------------

A 24 V relay coil of 120 ohm and 0.6 H.

.. GENERATED FROM PYTHON SOURCE LINES 30-38

.. code-block:: Python


    V, R, L = 24.0, 120.0, 0.6
    tau = rl_time_constant(L, R)
    t = np.linspace(0, 6 * tau, 3001)
    i_on = rl_current(V, R, L, t)
    print(f"tau = L/R = {1e3 * tau:.1f} ms; i(tau) = {1e3 * rl_current(V, R, L, tau):.1f} mA of {1e3 * V / R:.0f} mA")
    assert np.isclose(rl_current(V, R, L, tau), (V / R) * (1 - np.exp(-1)))





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

 .. code-block:: none

    tau = L/R = 5.0 ms; i(tau) = 126.4 mA of 200 mA




.. GENERATED FROM PYTHON SOURCE LINES 39-41

Energy balance
--------------

.. GENERATED FROM PYTHON SOURCE LINES 41-48

.. code-block:: Python


    supplied = trapezoid(V * i_on, t)
    dissipated = trapezoid(R * i_on**2, t)
    stored = 0.5 * L * i_on[-1] ** 2
    print(f"supplied {1e3 * supplied:.3f} mJ = dissipated {1e3 * dissipated:.3f} mJ + stored {1e3 * stored:.3f} mJ")
    assert np.isclose(supplied, dissipated + stored, rtol=1e-6)





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

 .. code-block:: none

    supplied 120.059 mJ = dissipated 108.119 mJ + stored 11.941 mJ




.. GENERATED FROM PYTHON SOURCE LINES 49-54

Switching off through a freewheeling path
-----------------------------------------

The coil current decays from its final value with the same time constant,
and the stored energy ends up in the resistance.

.. GENERATED FROM PYTHON SOURCE LINES 54-67

.. code-block:: Python


    i_off = rl_current(0.0, R, L, t, i0=V / R)
    assert np.isclose(trapezoid(R * i_off**2, t), 0.5 * L * (V / R) ** 2, rtol=1e-4)

    fig, ax = plt.subplots(figsize=(7, 3.6))
    ax.plot(1e3 * t, 1e3 * i_on, label="switch on")
    ax.plot(1e3 * (t + t[-1]), 1e3 * i_off, label="switch off")
    ax.axvline(1e3 * tau, color="gray", ls=":", lw=0.8)
    ax.set(xlabel="time [ms]", ylabel="coil current [mA]", title="RL current rise and decay")
    ax.legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/transients/images/sphx_glr_plot_02_helmholtz_rl_current_001.png
   :alt: RL current rise and decay
   :srcset: /api/gallery/electrical_engineering/transients/images/sphx_glr_plot_02_helmholtz_rl_current_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.072 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_transients_plot_02_helmholtz_rl_current.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/transients/plot_02_helmholtz_rl_current.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_helmholtz_rl_current.ipynb <plot_02_helmholtz_rl_current.ipynb>`

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

      :download:`Download Python source code: plot_02_helmholtz_rl_current.py <plot_02_helmholtz_rl_current.py>`

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

      :download:`Download zipped: plot_02_helmholtz_rl_current.zip <plot_02_helmholtz_rl_current.zip>`


.. only:: html

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

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