Keyword
Transient,Resistor Capacitance Inductance,Circuit,Discharge,Resistance,Voltage,Time.
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Reference
[1]:阿部節次:『実用電子公式集』,啓学出版,pp.64,1972.
[2]:内田知二・岡本久信:『MKS電気工学公式集』,オーム社,pp.81,1955
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Remarks
・LaTeX: \begin{cases}
\begin{cases}
& R^{2}-\frac{4L}{C}> 0\; , i\left ( A \right )=-\frac{2E}{\sqrt{R^{2}-\frac{4L}{c}}}e^{-\alpha t}\textup{sinh}\beta t\\
& R^{2}-\frac{4L}{C}= 0\; , i\left ( A \right )=-\alpha ^{2}CEte^{-\alpha t}\\
& R^{2}-\frac{4L}{C}< 0\; , i\left ( A \right )= -\frac{2E}{\sqrt{\frac{4L}{c}-R^{2}}}e^{-\alpha t}\textup{sin}\beta{}' t
\end{cases}
・LaTeX: \begin{cases}
& R^{2}-\frac{4L}{C}> 0\; , q\left ( C \right )=CEe^{-\alpha t}\left \left ( \cosh\beta t+\frac{\alpha }{\beta }\sinh\beta t \right ) \\\
& R^{2}-\frac{4L}{C}= 0\; , q\left ( C \right )=CEe^{-\alpha t}\left ( 1+\alpha t \right )\\
& R^{2}-\frac{4L}{C}< 0\; , q\left ( C \right )=CEe^{-\alpha t}\left \left ( \cos\beta{}' t+\frac{\alpha }{\beta {}'}\sin\beta{}' t \right ) \\
\end{cases}
・LaTeX: \alpha =\frac{R}{L}\; ,\beta =\sqrt{\left ( \frac{R}{2L} \right )^{2}-\frac{1}{LC}}\; ,\beta{}' =\sqrt{\left \frac{1}{LC}-( \frac{R}{2L} \right )^{2}}
・Making above Equation Image is powered by CODECOGS
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