A simple series RLC circuit with a voltage source Vs.

RLC Circuit with Battery Model

The RLC Circuit with Battery model simulates a resistor R, a capacitor C, and an inductor L in series with a battery and plots the time dependence of the voltage drops across these elements.  The resistance R reflects all sources of energy losses in the circuit.  The differential equation for the charge on the capacitor Q can be found by applying Kirchhoff's loop rule.

Because we are solving a dynamical model, transients are observed when the simulation is running and the battery voltage is changed.  The time step parameter Δt sets the time increment between voltage measurements and the number of points parameter n sets the amount of data that will be displayed.  The plot scrolls after n data points have been saved because data taken at earlier times is dropped.

Exercises:

1. Run the model and observe what happens as you toggle the battery voltage.  Increase the value of the time step between data points to Δt = 5.0E-3 and observe how the display changes as you toggle the battery voltage.  How are Δt and n related to the time sweep on an oscilloscope?
2. Change the inductance (L), resistance (R) and capacitance (C). Observe that the plot shows the source voltage (gray) as well as the voltages across each circuit element (color coded to the the input boxes at the top of the window).
3. Pick a specific point in time and measure each of the voltages and verify that the voltage across the inductor (red), resistor (green) plus capacitor (blue) do indeed equal the value of the source voltage (gray).
4. Describe what happens to the voltage across each element immediately after the voltage source switches.  Explain your observation.
5. The free oscillation frequency of undamped oscillations is given by ω_o=(LC)^-1/2. Set the resistance to zero and measure this oscillation period.  Pick different values of L and C and observe the new frequency. Are the inductor and capacitor voltages the same? Explain.
6. Due to energy losses, the frequency of free oscillations ω becomes lower ω²= ω_o²- γ² where γ=R/2L.  How do the curves change when resistance is increased and ω_o<γ?

References:

• Robert A. Morse, "Conceptualizing ideal circuit elements in the AP Physics C syllabus," The Physics Teacher 43 (8), pages 540-543 (2005)

• Yaakov Kraftmakher, "Demonstrations with an LCR Circuit," The Physics Teacher, 49(3) pages 168-170 (2011).

Credits:

The RLC Circuit with Battery model was developed by Wolfgang Christian using version 4.3 of the Easy Java Simulations (EJS) authoring and modeling tool.  You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file.  Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS.  You must, of course, have EJS installed on your computer.

Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.