Leak resistance across a spherical cell

Through what resistance does the charge on a sphere-in-sphere cell leak away?

The formula

R = \frac{1}{2 π \cdot σ} (\frac{1}{a} - \frac{1}{b})

LaTeX

R = \frac{1}{2\pi \cdot σ} \left( \frac{1}{a} - \frac{1}{b} \right)

Work it out

Fill from a part the library

a Inner sphere diameter

The inner electrode's outside diameter.

b Outer sphere diameter

The outer electrode's inside diameter.

σ Water conductivity

µS/cm

What a conductivity meter reads.

or see a worked example with typical numbers

Convert the diameters to metres and the conductivity to siemens per metre.
The resistance between concentric spheres of radii r_a and r_b through a conductor is (1/(4πσ))(1/r_a − 1/r_b). Written in diameters the 4π becomes 2π, which is the form above.

Two complete concentric spheres of uniform water; the stem and filler port are ignored.
The meter's conductivity, uniform and at DC — see the tubular leak calculation.