Key Equations

Key Equations

Capacitance	$C=\frac{Q}{V}$
Capacitance of a parallel-plate capacitor	$C={\epsilon }_0\frac{A}{d}$
Capacitance of a vacuum spherical capacitor	$C=4\pi {\epsilon }_0\frac{R_1{R}_2}{R_2-R_1}$
Capacitance of a vacuum cylindrical capacitor	$C=\frac{2\pi {\epsilon }_{0}l}{\text{ln}(R_2\text{/}{R}_1)}$
Capacitance of a series combination	$\frac{1}{C_{\text{S}}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\text{⋯}$
Capacitance of a parallel combination	$C_{\text{P}}=C_1+C_2+C_3+\text{⋯}$
Energy density	$u_E=\frac{1}{2}{\epsilon }_0{E}^2$
Energy stored in a capacitor	$U_C=\frac{1}{2}{V}^{2}C=\frac{1}{2}\frac{Q^2}{C}=\frac{1}{2}QV$
Capacitance of a capacitor with dielectric	$C=\kappa C_0$
Energy stored in an isolated capacitor with dielectric	$U=\frac{1}{\kappa }{U}_0$
Dielectric constant	$\kappa =\frac{E_0}{E}$
Induced electrical field in a dielectric	${\overrightarrow{E}}_{\text{i}}=\left(\frac{1}{\kappa }-1\right){\overrightarrow{E}}_0$