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Resistance Capacitance Analogy

Consider two metallic conductors in a homogeneous ohmic medium of conductivity σ. If a potential difference V is applied between these conductors, then the current is given by
        i = V/R,                                        … (1)
Here, R is the resistance of the medium.
The current i is given by,
    V/R = i = ∫s  j.dS = ∫s σE. dS = σ∫s E.dS.                            … (2)
Similarly, the charge q may be written by Gauss’ law,
    q = Φs ε E.dS
or    q = εV/σR,                                        … (3)
Here, ε is the permittivity of the medium between the conductors.
The capacitance can be written as
    C = q/V = ε/σR
. :    RC = ε/σ
Or    R = ε/σC                                        … (4)

If the capacitance between two conductors separated by a medium of permittivity ε is known, then the resistance between the same two conductors separated by a medium of conductivity σ may be calculated by means of Eq. (4).

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