# 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.

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### 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

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