The Inductance of Your Electrode!

 

 

 

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Even a single, straight piece of wire has some inductance!
We generally associate inductance with a loop or coil of wire. However, even a straight piece of wire, or your electrode, has some self-inductance. This can be important if you are dealing with low impedances (< 1 ohm) at high frequencies (> 10kHz).

My good, old 1962-63 edition of the CRC Handbook is a wealth of information! It contains a section on "Radio Formulae" (ref 1) that gives the inductance of a straight piece of round wire or rod: 

equation for wire inductance

In this equation, L is the inductance in nH (10-9 henry), l is the length and d is the diameter of the wire/rod (both in cm). µ is the permeability of the material (=1.0, except for iron and other ferromagnetic materials).  
 

 

 

 

Wire Diameter (d)  =

Wire Length (l) =

Permeability (µ) =

(1.0 EXCEPT for IRON)

   

Inductance =

nH


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The calculator, above, actually uses a slightly more complicated form of the equation (ref 2). The differences are small, even for fairly "squat" electrodes with d / l of 0.2 (x~1.005). 

inductance of wire

Note: This equation applies to an isolated round wire far from a ground plane or earth. For other geometries, see references 2 or 4. It also applies to frequencies that are accessible to the electrochemist, generally <1MHz.



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REFERENCES
(1) "Handbook of Chemistry and Physics, 44th Ed.", Chemical Rubber Publishing Co., Cleveland, OH, 1962. Yes, I got it NEW.
(2) "Inductance Calculations", F. W. Grover, Dover Publications, 2004 .
(3) http://www.ee.scu.edu/eefac/healy/indwire.html
(4) http://home.san.rr.com/bushnell/self_inductance.htm
 

 

 

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