The electrical resistance is represented by the symbol ‘R’ and it is measured in ohm (Ω) which is in terms of SI. The electrical resistance of any object is directly proportional to its length, l, and inversely proportional to its area of cross section, A.

That is, R ∝ \(\frac{l}{A}\) or R = ρ\(\frac{l}{A}\) 

The constant of proportionality, ρ (Greek, rho), is called resistivity (specific resistance). Its SI units are ohm metre (Ω m) and quite often its submultiple, ohm centimetre (Ω cm) is also used. IUPAC recommends the use of the term resistivity over specific resistance. Physically, the resistivity for a substance is its resistance when it is one metre long and its area of cross section is one m² .

It can be seen that: 1 Ω m = 100 Ω cm or 1 Ω cm = 0.01 Ω m The inverse of resistance, R, is called conductance, G, and we have the relation:

G = \(\frac{1}{R}\) = \(\frac{A}{ρl}\) = κ\(\frac{A}{l}\). The SI unit of conductance is siemens, represented by the symbol ‘S’ and is equal to ohm^–1 (also known as mho) or Ω ^–1. The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, κ (Greek, kappa). IUPAC has recommended the use of term conductivity over specific conductance and hence we use the term conductivity. The SI units of conductivity are S m^–1 but quite often, κ is expressed in S cm^–1. Conductivity of a material in S m^–1 is its conductance when it is 1 m long and its area of cross section is 1 m² . It may be noted that 1 S cm^–1 = 100 S m^–1 .

If the distance between two electrodes gets doubled and area of cross-section of electrode gets halved, then how many times the cell constant of the cell gets affected? 

Increased by four times.

σ = \(\frac{l}{A}\) ⇒ \(\frac{σ_2}{σ_1}\) = \(\frac{l_2}{l_1}\)x\(\frac{A_1}{A_2}\) = \(\frac{2l_1}{l_1}\)x\(\frac{A_1}{A_1/2}\) = 4

Hence, cell constant gets increased by four times.