Summary: Energy Storage (short)
This chapter summarises all formulas on energy stores for the ISD degree programme. This is a reduced summary; the ETR and BMT degree programmes have more formulas here.
\[
\begin{gathered}
\text{Capacitor:} \\[4pt]
C = \varepsilon_0 \cdot \varepsilon_r \cdot \frac{A}{d} \text{ with } \varepsilon_0 = 8.854 \cdot 10^{-12}\,\frac{\mathrm{As}}{\mathrm{Vm}} \\[6pt]
u_C(t) = U_{C0} + \frac{1}{C} \cdot \int i_C(t)\,dt \\[6pt]
i_C(t) = C \cdot \frac{du_C(t)}{dt} \\[6pt]
W_C = \frac{1}{2} C \cdot U_C^2 \\[4pt]
Q = C \cdot U
\end{gathered}
\]
\[
\begin{gathered}
\text{Inductor:} \\[4pt]
L = \mu_0 \cdot \mu_r \cdot N^2 \cdot \frac{A}{l} \text{ with } \mu_0 = 4\pi \cdot 10^{-7}\,\frac{\mathrm{Vs}}{\mathrm{Am}} \\[6pt]
i_L(t) = I_{L0} + \frac{1}{L} \cdot \int u_L(t)\,dt \\[6pt]
u_L(t) = L \cdot \frac{di_L(t)}{dt} \\[6pt]
W_L = \frac{1}{2} L \cdot I_L^2
\end{gathered}
\]
| Physical quantity | Symbol | Unit name | Unit symbol |
|---|---|---|---|
| Capacitance | \(C\) | Farad | \(\mathrm{F} = \dfrac{\mathrm{s}}{\Omega} = \dfrac{\mathrm{As}}{\mathrm{V}}\) |
| Inductance | \(L\) | Henry | \(\mathrm{H} = \Omega\mathrm{s} = \dfrac{\mathrm{Vs}}{\mathrm{A}}\) |