Transients in RLC-circuits calculated using the Ti-84 Plus
In RLC electric circuits, all kind of phenomena can occur (such as resonance). The behavior of the RLC circuit depends on the values of R, L and C. With the second order differential solver program and the post process program the phenomena can be investigated which is important for electrical engineering. Here, it is shown, that capacitor voltage, Uc, reaches 22.25 V which is about twice the supply voltage of 12 V.
For extra information about the second order differential equation solver, go to :
Example (see scheme) with: R1=10 Ω, L1=100 mH, C1=10 uF, V1=12V DC


Formulas for the electric circuit and applied in the Ti-Basic program


For this case, it yields :
y=Uc1, A=L1C1=1E-6, B-=R1C1=1E-4,
C=1, f(x) =12V
For numerical processes, the step size is an important parameter. Follow these rules:
Step size dx < √(A/C) /100 = √((1E-6))/100 =0.001/100=1E-5 sec or dx <(B/C)/20 = 0.025 sec
Take the smallest step size of dx which is dx=0.00001=1E-5 sec for this example.
The result obtained with the with Ti show that at 3.12 msec maximum capacitor voltage = 22.25 V and The Ti results approach the results of Multisim and the analytical solution extremely well. At t=0.22 sec Values of the numerical program and the analytical solution agree.

Results Multisim analytical solution


For questions or a request for the program, mail to frieboon@gmail.com or chat and the program will be sent. Don't forget to include your email address!!