The step response of a parallel R L C circuit is
$v=10+20 e^{-300 t}(\cos 400 t-2 \sin 400 t) \mathrm{V}, \quad t \geq 0$
when the inductor is 50 $\mathrm{mH}$ . Find R and C.

Question

The step response of a parallel R L C circuit is
v=10+20 e^{-300 t}(\cos 400 t-2 \sin 400 t) \mathrm{V}, \quad t \geq 0
when the inductor is 50 \mathrm{mH}. Find R and C.

Accepted Answer

[latex]\alpha=300=\frac{1}{2 R C} (1)[/latex]
[latex]\omega_{d}=\sqrt{\omega_{o}^{2}-\alpha^{2}}=400 \quad \longrightarrow \quad \omega_{o}=\sqrt{400^{2}-300^{2}}=264.575=\frac{1}{\sqrt{L C}} (2)[/latex]
From (2),

C=[latex]\frac{1}{(264.575)^{2} imes 50 imes 10^{-3}}=285.71 \mu \mathrm{F}[/latex]

From (1)
[latex]R=\frac{1}{2 \alpha C}=\frac{1}{2 imes 300}(3500)=5.833 \Omega[/latex]

Question 8.52: The step response of a parallel R L C circuit is v=10+20 e^-...

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