Chapter 23: Capacitance

A capacitor's defining property is its capacitance, quantified as the ratio of stored charge to applied potential difference and measured in farads. The chapter establishes that energy storage within a capacitor depends on both the charge accumulated and the voltage applied, with three equivalent mathematical expressions allowing calculation based on different known variables. The energy stored scales with the square of the applied voltage, meaning that modest increases in voltage produce disproportionately larger energy storage. When multiple capacitors are combined in circuits, their effective capacitance follows rules inverse to those governing resistors: parallel arrangements produce additive capacitance while series arrangements require reciprocal summation. A critical phenomenon occurs when charged and uncharged capacitors are connected in parallel while isolated from external power supplies, causing charge redistribution that conserves total charge but dissipates energy as heat in conducting wires. All conductors, including isolated spherical objects such as Van de Graaff generator domes, inherently possess capacitance proportional to their physical dimensions. The chapter also addresses the dynamic behavior of capacitors during discharge through resistive pathways, demonstrating that charge, voltage, and current decay exponentially rather than instantaneously. The time constant, derived from the product of capacitance and resistance values, determines the rate at which these quantities diminish toward zero, enabling quantitative prediction of discharge behavior across diverse practical applications in electrical systems.