Calculation of Transient：Resistor Capacitance Inductance Circuit-Discharge.

Keyword Transient,Resistor Capacitance Inductance,Circuit,Discharge,Resistance,Voltage,Time.

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

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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