Experiment 4: LCR Circuit.

Text Box: Expt. 1. Simple Harmonic Motion Text Box: List of Experiments (click the buttons for each expt.) Text Box: Expt. 3. LC circuit Text Box: Expt. 2. Damped Simple Harmonic Motion Text Box: Expt. 8. Nonlinear Damped Oscillation Text Box: Expt. 4. LCR Circuit Text Box: Expt. 5. Resonance in LCR Circuit Text Box: Expt. 6. Coupled Simple Harmonic Motion Text Box: Expt. 7. Nonlinear Oscillation

LCR circuit

RLC series circuit.png

For the case where the source is an unchanging voltage, the second order differential equation governing the current in the LCR circuit is :

{{d^2 i(t)} \over {dt^2}} +{R \over L} {{di(t)} \over {dt}} + {1 \over {LC}} i(t) = 0

 

For the RLC circuit, there are two important parameters,

\alpha = {R \over 2L}   and \omega_0 = { 1 \over \sqrt{LC}}

 

is the natural frequency of the circuit.

A useful parameter is the damping factor, ζ which is defined as the ratio of these two,

\zeta = \frac {\alpha}{\omega_0}

The general solution of the differential equation is an exponential in either root or a linear superposition of both,

i(t) = A_1 e^{s_1 t} + A_2 e^{s_2 t}

where,

s_1 = -\alpha +\sqrt {\alpha^2 - {\omega_0}^2}

s_2 = -\alpha -\sqrt {\alpha^2 - {\omega_0}^2}

Based on above one gets different condition of oscillatory response, via., underdamped, overdamped and critically damped.

 

For more details see

http://en.wikipedia.org/wiki/RLC_circuit

Please feel free to send your feedback, suggestions or queries regarding the experiment to: oscillations.vlab@gmail.com

In your email, please mention the experiment no. and name of the experiment.

 

 

 
Text Box: Make sure you have downloaded both the ‘LabVIEW Runtime engine’ and the ‘Vision Runtime Engine’ from the links provided in the main page. Text Box: go to Main Page Virtual Laboratory Oscillations

Developed and maintained by: Satyajit Banerjee, Pabitra Mandal and Gorky Shaw

Click here to download the step-by-step instructions video demonstration.

Click here to download the program to run on your computer locally offline (Recommended)

 Procedure for downloading and running programs offline:

· To download the programs, right click on the link above and choose ‘save target as’, or, ‘save link as’ depending on the browser.

· Save the ‘.zip’ file to any directory on your PC.

· Extract the ALL contents of the .zip file to the SAME folder.

· Double click on the file “LCR.exe” to start executing the program.

· After this, perform the experiment as demonstrated in the video instructions provided in the link below.