Showing posts with label inductor. Show all posts
Showing posts with label inductor. Show all posts

Tuesday, March 24, 2020

Dynamic Formulas for the Capacitor and for the Inductor


Charging the capacitor from the CV(=Vs) src. ::
The voltage drop on the series resistor \[V_R=V_S-V_C\]
\[t_{0_{↑}^{↑}→V_C}=-R·C·ln\left({1-\frac{V_C}{V_S}}\right)=R·C·ln\frac{V_S}{V_R}\]
\[t_{V_{1_C}{}_{↑}^{↑}→V_{2_C}}=R·C·ln\frac{V_S-V_{1_C}}{V_S-V_{2_C}}=R·C·ln\frac{V_{1_R}}{V_{2_R}}\]
Dis-charging the capacitor through a fixed value resistor ::
\[t_{V_{2_C}{}_{↓}^{↓}→V_{1_C}}=-R·C·ln\frac{V_{1_C}}{V_{2_C}}=R·C·ln\frac{V_{2_C}}{V_{1_C}}\]

"Charging" the inductor from the CV(=Vs) src. ::
The peak current \[I_{MAX}=\frac{V_S}R\]
\[t_{0_{↑}^{↑}→I_L}=-\frac LR·ln\left({1-\frac{I_L}{I_{MAX}}}\right)\]
\[t_{I_{1_L}{}_{↑}^{↑}→I_{2_L}}=\frac LR·ln\frac{I_{MAX}-I_{1_L}}{I_{MAX}-I_{2_L}}\]
"Dis-charging" the inductor through a fixed value resistor ::
\[t_{I_{2_L}{}_{↓}^{↓}→I_{1_L}}=\frac LR·ln\frac{I_{2_L}}{I_{1_L}}\]


[Eop]