🔋 Capacitor Lab

Parallel Plate

$$ C = \frac{\kappa \epsilon_0 A}{d} $$

$$ E = \frac{V}{d} $$

Cylindrical

$$ C = \frac{2\pi \kappa \epsilon_0 L}{\ln(b/a)} $$

$$ E_{max} = \frac{V}{a \ln(b/a)} $$

Spherical

$$ C = 4\pi \kappa \epsilon_0 \left( \frac{ab}{b - a} \right) $$

$$ E_{max} = \frac{V}{a^2 \cdot (1/a - 1/b)} $$

General & Circuits

$$ Q = CV \quad\quad U = \frac{1}{2}CV^2 $$

$$ C_{Series} = \left( \sum \frac{1}{C_i} \right)^{-1} $$

$$ C_{Parallel} = \sum C_i $$