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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

Scheme of RLC circuit with the corresponding differential equatione e
Capacitor voltage equation of RLC circuit

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

Differential equation for RLC circuit
Differential equation solved by your TI

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 of the 2nd differential equation solver compared with analytical solution

 Results Multisim                                                          analytical solution

RLC analysis with Multisim for check of the Ti results
analytical solution of 2nd order differential equation compared with solution of TI84 calculator

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

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