the resistor assuming that every element of the surface will receive a power equal to the sum of the electric power dissipated in each the volume units p o located beneath it and will then transfer it into its environment with this principle the thickness profile of the transition section 4 could be determined in a such a way that the electrical power produced by unit of surface is approximately the same whatever the surface unit considered in a more detailed way the thickness profile could be determined by assuming that in a steady state situation the power dissipated by each surface unit is equal to the electric power po dissipated below the same surface unit and using the equation po u03b4u 2 r u00d7 s where u03b4u is the difference of electric potential between the two extremities of a given surface unit r the electrical resistance between these two extremities and s the area of the surface unit the value of po can be calculated using the following simplified formulas where ua and ub are the two equipotential lines lt lt a gt gt and lt lt b gt gt shown on the fig4 respectively u03c1 is the resistivity of the carbonaceous material and r e dr are the average radius of the transition section around the center c u2032 the thickness and the width of each infinitesimal step i respectively the power po by unit of surface is then.