Question

3· In a co-axial cylindrical system, the insulation material that is going to be used has a breakdown strength of E,0 kVc. In this contiguration, 10 kV is applied to the inner conductor. Determine the inner and outer conductor's radii considering the optimum geometry with regard to breakdown. Determine maximum and minimum electric field strengths aud system capacitance 8851 x 10 F/

Answer 1

Given that coaxial. cylindrical system with inner radius (r) and outer radius(R). v rightarrow is the potential of inner conductor with Respect to the outer conductor The electric field intensity E at a distance x from the center of the conductor is. E = lambda/2pi epsilon x. Now V = integral^R_t E dr = integral^R_r lambda/2 pi E x dx. = lambda/2 pi E Vertical-bar ln x Vertical-bar ^R_r V = lambda /2 pi E [ln R - ln r] v = lambda/2pi E ln (R/r) \r\n Now 'E' can be written as D = (lambda/2 pi E) times 1/x = v/ln(R/x) times 1/x = v/x ln(R/r) Given In the problem it is said to consider optimum geometry with respect to breakdown to determine inner and outer radius According to this R/r = c = 2.118 Given, The insulation material breakdown strength = 80 kv/m. This is the maximum dielectric strength and it is E_max = V/r ln (R/r) rightarrow maximum dielectric strength and it is E_max