Farad
In 1746 in Leiden, Pieter van Musschenbroek poured water into a glass jar and lowered a wire into it. It was charged from an electrical machine. An assistant held the jar in one hand and touched the wire with the other. The shock was so strong that Musschenbroek wrote to a colleague that he would not repeat the experiment for anything.
The jar turned out to be the first capacitor: the water inside and the hand outside were the two plates, and the glass between them the insulator. How much charge the plates hold at a given voltage is shown by the capacitance. One farad is the capacitance to which a voltage of 1 V gives a charge of 1 C. That is a great deal: the whole Earth, as a sphere, has a capacitance of about 710 µF.
| Notation | F |
| Definition | coulomb per volt · C/V · kg⁻¹·m⁻²·s⁴·A² |
| Reference values | ε₀ — 8.854 187 8·10⁻¹² F/m · a sphere of radius 1 m — 111 pF · the Earth as a sphere — about 710 µF |
| Introduced | 1881, International Electrical Congress in Paris · in the SI since 1960 |
| Standards | ISO 80000-6 · IEC 60384 · IEC 60062 · SI Brochure 9th ed. |
| Typical values | 10 pF — an oscilloscope probe · 100 nF — next to a chip's pins · 3000 F — a supercapacitor |
01 · Definition
A coulomb for every volt
Capacitance C shows how much charge must be put on a conductor to raise its voltage by one volt. It is easiest to see with two plates. One receives plus, the other minus, and a field appears between them. The larger the plates and the closer they are to each other, the more charge they hold at the same voltage.
An insulator between the plates increases the capacitance. Its molecules turn in the field and partly cancel it. Glass increases the capacitance about 7 times, barium titanate ceramic a thousand times and more. The stored energy grows as the square of the voltage.
What “104” means on a tiny capacitor
A ceramic disc has room for three digits and a letter. The first two digits are the start of the number. The third is how many zeros to add to it. Together they give the capacitance in picofarads. The letter after the digits is the tolerance. Choose the digits, and the capacitance with its limits appears below.
To get 1 F from two plates with a 1 mm air gap, each plate would have to cover 113 km². An isolated sphere of 1 F would have a radius of 9 million km. Supercapacitors get round this differently. Their charge sits on the surface of porous carbon, and the gap between the charges is about a nanometre. One gram of such carbon has hundreds of square metres of surface.
Why a spark jumps when the glass is pulled out of a capacitor
On the left is a high-voltage supply up to 15 kV; it charges two square plates 20 × 20 cm through a 100 MΩ resistor. The red plate is plus, the turquoise one minus. The yellow lines are the field between them: the denser the lines, the stronger the field. To the right of the plates a bar compares the field with the strength of air, about 3 kV/mm. An insulator can be slid between the plates. The magnifier on the right shows its molecules: the red end is plus, the turquoise end minus. The supply can be disconnected: then the charge has nowhere to go. The “Discharge” button gives the energy to a lamp.
The supply is charging the plates.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
“MFD” on old capacitors means microfarads, not millifarads. Picofarads were written “MMFD” — micromicrofarads.
A 3000 F supercapacitor at 2.7 V stores about 11 kJ. That is roughly as much as an alkaline AA battery.
The capacitance of the whole Earth, about 710 µF, is less than that of a single 1000 µF filter capacitor in a power supply.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
In 1956 Andrew Thompson and Douglas Lampard found a capacitor whose capacitance can be calculated. Four long cylinders stand at the corners of a square. The capacitance between opposite pairs per metre of length equals ε₀·ln 2 / π, about 1.953 549 pF/m. This holds for almost any exact symmetry of the cross-section. The length is measured with a laser interferometer, and the capacitance follows from the length.
Since 2019 the constants h and e are exact, and the farad is linked to them through the ohm. A quantum Hall resistance standard is compared with a capacitor in a quadrature bridge at a known frequency: C = 1 / (2πfR). This is how national laboratories realise the farad to parts per million.
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