.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrochem/battery/plot_01_discharge_curves.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_electrochem_battery_plot_01_discharge_curves.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_electrochem_battery_plot_01_discharge_curves.py:


Peukert's law: battery capacity falls at high discharge rates
===============================================================

Peukert's 1897 power law, :math:`t = C_p/I^k`, says a lead-acid battery
discharged faster delivers less total charge. Using
:func:`~chemistrykit.electrochem.systems.battery.effective_capacity`, this
example compares the ideal Peukert exponent k=1 (same capacity at every
rate) with a realistic k=1.2, then draws discharge curves from
:class:`~chemistrykit.electrochem.systems.battery.ConstantCurrentBattery`
(a deliberately simplified model; see its docstring) whose runtimes
shrink faster than 1/I.

.. GENERATED FROM PYTHON SOURCE LINES 16-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.electrochem.systems.battery import ConstantCurrentBattery, effective_capacity
    from chemistrykit.electrochem.visualizers.electrochem_plots import plot_discharge_curve








.. GENERATED FROM PYTHON SOURCE LINES 23-24

Ideal (k=1) vs. real (k=1.2) Peukert-law effective capacity vs. rate.

.. GENERATED FROM PYTHON SOURCE LINES 24-38

.. code-block:: Python

    currents = np.linspace(0.2, 5.0, 30)
    C_p = 10.0
    C_eff_ideal = effective_capacity(C_p, currents, k=1.0)
    C_eff_real = effective_capacity(C_p, currents, k=1.2)

    fig, ax = plt.subplots()
    ax.plot(currents, C_eff_ideal, label="k=1.0 (ideal)")
    ax.plot(currents, C_eff_real, label="k=1.2 (typical lead-acid)")
    ax.set_xlabel("Discharge current (A)")
    ax.set_ylabel("Effective delivered capacity (Ah)")
    ax.set_title("Peukert's law: capacity fade at high discharge rate")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/electrochem/battery/images/sphx_glr_plot_01_discharge_curves_001.png
   :alt: Peukert's law: capacity fade at high discharge rate
   :srcset: /api/gallery/electrochem/battery/images/sphx_glr_plot_01_discharge_curves_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 39-41

Discharge curves at a few different constant currents, all from the
same Peukert capacity constant.

.. GENERATED FROM PYTHON SOURCE LINES 41-49

.. code-block:: Python

    fig2, ax2 = plt.subplots()
    for current in (0.5, 1.0, 2.0):
        battery = ConstantCurrentBattery(capacity_peukert=C_p, current=current, v_nominal=3.7, internal_resistance=0.05, k=1.2)
        plot_discharge_curve(battery, ax=ax2, label=f"I = {current} A")
    ax2.legend()
    fig2.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/electrochem/battery/images/sphx_glr_plot_01_discharge_curves_002.png
   :alt: Constant-current discharge curve
   :srcset: /api/gallery/electrochem/battery/images/sphx_glr_plot_01_discharge_curves_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.080 seconds)


.. _sphx_glr_download_api_gallery_electrochem_battery_plot_01_discharge_curves.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_discharge_curves.ipynb <plot_01_discharge_curves.ipynb>`

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

      :download:`Download Python source code: plot_01_discharge_curves.py <plot_01_discharge_curves.py>`

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

      :download:`Download zipped: plot_01_discharge_curves.zip <plot_01_discharge_curves.zip>`


.. only:: html

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

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