.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_03_rc_discharge.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_03_rc_discharge.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_03_rc_discharge.py:


RC discharge
============

A capacitor discharges through a known resistor. The voltage decays exponentially towards
a small offset of the measuring device. From the time constant τ = RC we obtain the
capacitance.

.. GENERATED FROM PYTHON SOURCE LINES 11-23

.. code-block:: Python

    import numpy as np

    import fitwise as fw

    rng = np.random.default_rng(3)
    t = np.linspace(0, 50, 60)  # ms
    voltage = 4.8 * np.exp(-t / 12.5) + 0.12 + rng.normal(0, 0.02, t.size)  # V

    model = fw.models.exponential + fw.models.constant
    result = fw.fit(model, t, voltage, yerr=0.02)
    print(result)





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

 .. code-block:: none

    Model:      exponential(x; amp, tau) + constant(x; c)
    Method:     Trust Region Reflective (scipy least_squares) (auto: nonlinear)
    Converged:  yes (27 evals)
    Data:       60 points, yerr given (absolute)
    Start:      amp, tau: log-linear fit · c: edge baseline

    Parameter    Value   ± Std.Err    Rel.   Bounds
    amp          4.794       0.010   0.2 %   –
    tau         12.538       0.067   0.5 %   –
    c           0.1180      0.0064   5.4 %   –

    χ²/ndf = 1.2 (57 dof, p = 0.14)    R² = 0.99971    AIC = 13.8
    Correlations > 0.5:  tau–c (-0.83)
    Warnings:   none




.. GENERATED FROM PYTHON SOURCE LINES 24-27

The ``Start:`` line of the report shows how the starting values were found: the offset
``c`` from the flat end of the curve (``edge baseline``), the decay from a log-linear fit
of the rest.

.. GENERATED FROM PYTHON SOURCE LINES 27-31

.. code-block:: Python

    fig, axes = result.plot()
    axes[0].set_ylabel("U (V)")
    axes[1].set_xlabel("t (ms)")




.. image-sg:: /auto_examples/images/sphx_glr_plot_03_rc_discharge_001.png
   :alt: plot 03 rc discharge
   :srcset: /auto_examples/images/sphx_glr_plot_03_rc_discharge_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 18.503588541666666, 't (ms)')



.. GENERATED FROM PYTHON SOURCE LINES 32-33

Capacitance with R = 10.0 kΩ (assumed exact). τ is in ms, so C comes out in µF.

.. GENERATED FROM PYTHON SOURCE LINES 33-36

.. code-block:: Python

    R = 10.0  # kΩ
    tau = result.params["tau"]
    print(f"C = {tau.value / R:.4f} ± {tau.stderr / R:.4f} µF")




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

 .. code-block:: none

    C = 1.2538 ± 0.0067 µF





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

   **Total running time of the script:** (0 minutes 0.116 seconds)


.. _sphx_glr_download_auto_examples_plot_03_rc_discharge.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_rc_discharge.ipynb <plot_03_rc_discharge.ipynb>`

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

      :download:`Download Python source code: plot_03_rc_discharge.py <plot_03_rc_discharge.py>`

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

      :download:`Download zipped: plot_03_rc_discharge.zip <plot_03_rc_discharge.zip>`


.. only:: html

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

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