Express the relation among cell constant, resistance of the solution in the cell, and conductivity of the solution. How is molar conductivity of a solution related to its conductivity?

G = 1/R
K = G × G*
Substitute the value of conductance in the above equation
K = (1/R) × G*
R = 1/(G × G*)
Molar conductivity is defined as the conductivity of an electrolyte solution divided by the molar concentration of the electrolyte, and so measures the efficiency with which a given electrolyte conducts electricity in solution.
Λm = K × V
Where,
G = conductance
G* = cell constant
K = conductivity
Λm = molar conductivity
G* × 1/2 = K => G* = RK
Λm = k × 1000/C S cm²mol⁻¹