Studying colonial-era capacitor

Article By : John Dunn

Looking at an 18th century capacitor and its application is definitely a study in trailing-edge technology, but it can still be instructive.

When Benjamin Franklin performed his kite experiment in the midst of an electrical thunderstorm and lived for many more years to tell the tale, the device he had at hand to store electric charge was called a Leyden jar. Today, we would call that device a capacitor.

There is a nice treatise on Leyden jars on Wikipedia, where mention is made of a typical capacitance in jars of that era as 1 nF, which equals 1000 pF. By making just a few plausible assumptions about physical dimensions from looking at colonial era drawings, that capacitance can be estimated as seen in the following sketch and calculations.

annotated diagram of a Leyden jarFigure 1 This Leyden jar diagram is based on colonial era drawings.

Let vertical height = 8 inches
Let diameter = 4 inches
Then radius = 2 inches

Cylindrical area = circumference × heightc
Cylindrical area = π × diameter × height
Cylindrical area = π × 4 × 8 = 100.53 –> 100 in2

Disk area = π × radius2 + π × 22 = 12.57 –> 13 in2

Total area = 113 in2

Assume the glass thickness is ¼ inch.

Dielectric constant of glass is between 3.7 and 10.
Permittivity of free space = e0 = 8.854 pF/meter
Permittivity of free space = e0 = 0.225 pF/inch

Cap = er × e0 × total area/glass thickness
Cap = 3.7 × 0.225 × 113/0.25 = 376 pF
Cap = 10 × 0.225 × 113/0.25 = 1017 pF

Approximate cap = 1000 pF

These things are reportedly capable of acquiring tens of kilovolts (20 kV to 60 kV in one essay) when charged up. That metal ball above the stopper helps guard against corona effects, which in my own high voltage experience will arise in the vicinity of 30 kV.

It is instructive to look at the stored energy that is involved. That energy is ½CV2, where C is capacitance in farads, V is voltage in volts, and energy is in joules. For 1000 pF at 60 kV, the energy = ½ × 1000E-12 × (600002) = 1.8 joules

That’s enough energy to hurt you, so experimenters with Leyden jars do have to be pretty darn careful.

This article was originally published on EDN.

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).

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