Where does capacitance collide?

The property of a conductor, or a pair of conductors, that measures how much electric charge it holds for each volt of potential difference across it, written C = Q/V and measured in farads. Maxwell's 1873 A Treatise on Electricity and Magnetism formalised the capacity of a conductor as a constant set by its size, its shape, and the insulating material around it. Here the referent is charge storage in a designed electrical component or geometry, counted in farads, and not a nerve membrane's parameter, a vein's blood volume, or an electrode interface.[1]

Unit

One capacitor's charge-to-voltage ratio, in farads (coulombs per volt)

Recovery means

The stored charge flows back into the circuit when the capacitor discharges, on a timescale set by the RC time constant

Measured by

Read with a capacitance meter or an LCR bridge, or computed from plate geometry and the dielectric permittivity

In a neuron, the thin insulating lipid bilayer of the cell membrane behaves as a capacitor, storing charge across itself, and this membrane capacitance sets how quickly the membrane voltage can change. Hodgkin and Huxley's 1952 quantitative model of the nerve impulse treated the membrane as a capacitance in parallel with its ion channels, with a specific value near one microfarad per square centimetre, so this term governs the timing of the action potential through the membrane time constant in cable theory. Although it is quoted in the same farads as a circuit capacitor, the referent is a biophysical parameter of living tissue, not a manufactured component, a vein's volume, or a chemical interface.[2]

Unit

A membrane's charge storage, as specific capacitance in microfarads per square centimetre

Recovery means

The charge held on the membrane is redistributed by ion currents as the membrane voltage returns toward rest

Measured by

Estimated from the membrane time constant, or by voltage-clamp and impedance recordings on the cell

In the circulation, capacitance is the volume of blood a vessel bed, chiefly the veins, holds for a given distending pressure, so the veins serve as a reservoir that buffers changes in the body's blood volume. Rothe's 1983 review Reflex control of veins and vascular capacitance described how the nervous system adjusts venous tone to shift blood between this reservoir and the actively circulating volume. This meaning is measured in millilitres per millimetre of mercury, not in farads, and its referent is fluid volume stored under pressure, unrelated to electric charge stored in a component or across a membrane.[3]

Unit

A vascular bed's stored blood volume per pressure, in millilitres per millimetre of mercury

Recovery means

Constriction of venous smooth muscle returns stored blood to the active circulation

Measured by

Assessed from paired volume and pressure changes, for example by mean circulatory filling pressure or limb plethysmography

At the boundary between an electrode and an electrolyte, ions gather into a thin electrical double layer that stores charge, giving a double-layer capacitance that underlies the supercapacitor. Grahame's 1947 review The electrical double layer and the theory of electrocapillarity set out the structure of this interface, and Conway's 1991 study distinguished this non-Faradaic charge storage from battery-like chemical reactions. Though also expressed in farads, often per gram of electrode material, the referent is charge held at a chemical interface by separated ions, not the capacity of a designed component, a nerve membrane, or a vein.[4][5]

Unit

An electrode interface's stored charge per voltage, in farads (often per gram of material)

Recovery means

The stored charge is released rapidly and reversibly as the double layer discharges

Measured by

Measured by cyclic voltammetry, galvanostatic charge-discharge, or electrochemical impedance spectroscopy