OpenStax University Physics/E&M/Capacitance

For quiz at QB/d_cp2.8
$$Q=CV$$ defines capacitance.

$$C=\varepsilon_0\tfrac A d$$ where A is area and d<<A1/2 is gap length of parallel plate capacitor

$$\text{Series}:\; \tfrac{1}{C_S} = \sum\tfrac{1}{C_i}.$$  $$\text{ Parallel:}\;C_P=\sum C_i.$$

$$u=\tfrac 1 2 QV = \tfrac 1 2 CV^2=\tfrac{1}{2C}Q^2$$ = stored energy

$$u_E=\tfrac 1 2 \varepsilon_0E^2$$ = energy density