.. 4.4

Transient response of LCR circuits
==================================

**Objective**

Explore the oscillatory nature of L and C in series. Resonant frequency
of series LC circuit is given by :math:`f_0 = 1/(2\pi\sqrt{LC})`. The damping
factor is :math:`R/(2\sqrt{LC})`, and it is equal to 1 for critical
damping (http://en.wikiversity.org/wiki/RLC\_circuit). Depending
upon the value of C/L and R, the response could be under-damped,
critically-damped or over-damped.

.. image:: schematics/RLCtransient.svg
	   :width: 300px
.. image:: pics/RLC-curves.png
	   :width: 300px

**Procedure**

-  Start with the coil and :math:`0,1~\mu F` capacitor
-  Click on 5->0V STEP. Adjust x-axis and repeat if required.
-  FIT the graph to find the resonant frequency & Damping.
-  Repeat with a resistor between OD1 and the inductor.
-  Repeat the experiment with different values of L, C and R

**Discussion**

We have used the 3000 turn coil and a :math:`0,1~\mu F` capacitor. The voltage
across the capacitor after a 5 to 0V step is shown in figure. The
measured resonant frequency tallies with :math:`f = 1/(2\pi\sqrt{LC})`,
within the component tolerance values.
