The Daraf: Reciprocal Capacitance and Electrical Elastance
Pair this resource with the farad explainer, the siemens overview, and the Ohm's law calculators to analyse circuits where reciprocal capacitance provides intuitive insight.
Introduction
The daraf (symbol: daraf) is the rarely used unit of electrical elastance—the reciprocal of capacitance. If a capacitor has a capacitance of C farads, its elastance is 1/C darafs. Elastance describes how much electric potential results from a unit electric charge on a capacitor, offering an alternative viewpoint to the more familiar capacitance representation.
Although the SI does not encourage naming reciprocal units separately, the daraf occasionally appears in theoretical discussions, older textbooks, and niche analyses where reciprocal relationships simplify algebra. Understanding the daraf clarifies dualities between electrical quantities and aids in analogies to mechanical systems where stiffness is the reciprocal of compliance.
Definition and Unit Relationships
Capacitance is defined as C = Q/V, the ratio of stored charge to voltage. Elastance is its reciprocal: S = V/Q, measured in darafs. In SI base units, one daraf equals one volt per coulomb, or equivalently one ohm per second because 1 F = 1 C/V and 1 Ω = 1 V/A. Expressing elastance in base units highlights its role in time-domain circuit behaviour.
Many engineers simply express elastance as 1/F, but naming the daraf emphasises symmetry across electrical quantities: conductance vs. resistance, susceptance vs. reactance, and elastance vs. capacitance. These analogies become useful when using network synthesis techniques or dual transformations in circuit theory.
SI Prefixes
Because practical capacitances span femtofarads to farads, elastance often spans from mega-darafs to pico-darafs. For example, a 100 nF capacitor has an elastance of 10⁷ darafs (10 mega-darafs). Using prefixes consistently avoids confusion when tabulating component values or performing quick hand calculations.
Historical Context
The term "daraf" emerged in the early 20th century as an anagrammatic counterpart to "farad," reflecting a broader trend of naming reciprocal units (such as "mho" for the reciprocal of the ohm). While the International Electrotechnical Commission eventually discouraged non-SI reciprocal unit names, the daraf remains a charming reminder of the era when engineers experimented with linguistic symmetry to aid intuition.
Even though modern standards prefer plain reciprocal notation, some analog circuit texts and filter design notes still reference elastance explicitly, especially when deriving dual network topologies. Recognising the terminology helps decode historical schematics and prevents misinterpretation when reviewing legacy documentation.
Daraf in Educational Materials
University courses sometimes reintroduce the daraf when teaching network duality or when emphasising the mathematical structure of Maxwell's equations. Students benefit from seeing how reciprocal relationships mirror each other across electrical parameters, reinforcing conceptual understanding beyond rote memorisation.
Concepts and Applications
Elastance proves useful when modelling small stray capacitances in high-impedance circuits. Summing elastances rather than capacitances simplifies calculations for capacitors connected in series, because series capacitances add reciprocally: the total elastance equals the sum of individual elastances. This perspective reduces algebraic complexity when dealing with sensor inputs, photodiode amplifiers, or precision filters.
Control engineers also use elastance when formulating state-space models of electrostatic actuators or piezoelectric devices, where stiffness analogies improve intuition. By expressing system matrices in terms of elastance, designers can more easily compare electrical behaviour with mechanical compliance or thermal resistance networks. The LED series resistor calculator illustrates how adjusting component values to manage current also alters effective elastance seen by driver circuits.
Frequency-Domain Analysis
In the frequency domain, capacitive reactance XC = 1/(ωC) has a direct relationship with elastance since S = ωXC when ω is angular frequency. Expressing design goals in darafs per radian can reveal proportional relationships between frequency tuning and component tolerances.
Practical Use Cases
Precision Instrumentation
Guarding techniques in electrometers and picoampere measurement equipment rely on understanding elastance to minimise leakage. Technicians evaluate cable and connector elastance to ensure that stray capacitance does not corrupt ultra-low current readings. The USB voltage drop calculator can be repurposed to estimate how distributed capacitance influences supply stability in sensitive instruments.
Power Electronics
High-frequency converters require careful management of parasitic capacitances. Expressing these parasitics in darafs aids in summing contributions from multiple components and predicting resonant frequencies. Designers use the Ohm's law voltage calculator to verify operating points when elastance variations shift impedance.
Signal Integrity
In high-speed digital design, controlled impedance traces depend on balancing inductance and capacitance per unit length. Expressing capacitance as elastance per metre allows direct comparison with inductive reluctance, streamlining characteristic impedance calculations. Engineers cross-check these relationships with Ohm's law current tools when validating driver capabilities.
Importance for Measurement Science
The daraf exemplifies the value of reciprocal thinking in engineering. While the unit is rarely listed in standards, recognising elastance encourages designers to evaluate systems from multiple perspectives, ensuring robust understanding of circuit behaviour.
Documenting elastance alongside capacitance facilitates communication between analog specialists, signal integrity engineers, and metrologists. Whether expressed explicitly in darafs or implicitly as 1/F, the concept remains crucial for precision electronics, high-frequency design, and historical literacy.