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Transformer Engineering - Design and Practice Episode 2

Tham khảo tài liệu 'transformer engineering - design and practice episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Appendix B Stress and Capacitance Formulae In this appendix formulae are derived for electric stress and capacitance for commonly existing electrode configurations in transformers such as two round electrodes or round electrode and plane. B1 Stress Calculations The information about the electric field intensity and potential field between two parallel cylindrical electrodes can be found by considering the respective equivalent line charges. Consider two line charges pL and -pL charges per unit length placed at x m and x -m respectively as shown in figure B1. Now due to single line charge pL the electric field intensity at a distance r is given by 2x8 r B1 where e is permittivity of medium. The potential reckoned from a distance R is u - Edr ln J 2x I r R v B2 The resultant potential at point A figure B1 due to line charges pL and-pL is _ Pl Pl Ư _ Pl I_r r Ì 2x8 r2 J 2x V n y r2 J B3 459 Copyright 2004 by Marcel Dekker Inc. 460 Appendix B Figure B1 Two line charges placed at x -m and x m Let us now find the nature of equipotential surface having potential of u. From equation B3 we get But from figure B1 we have -r2 Solving by componendo and dividendo By algebraic manipulations we get Copyright 2004 by Marcel Dekker Inc. Appendix B 461 B4 This is the equation of a circle with radius and center 5 o 2ti u m coth 0 I Pr J Thus the equipotential surface is a cylinder which intersects the x-y plane in a circle with radius r and center at ỉ 0 . From the above expressions for radius and center we get 5 I 2tĩ u ị ỹ cosh - B5 r Pl _ 2 2 2 1 21 u I ỈÌI 2 Also s -r m coth I------------------Y-----7- m sinh2 B6 I Pl By substituting the value of m in the equation for radius we have . I 2tĩ u I ys2-r2 _ sinh ------------- B7 I Pl J r Now from equations B5 and B7 we get Thus we get the expression for potential as B8 Now we will consider two parallel cylindrical conductors of radii R1 and R2 placed such that the distance between their centers is 2s. The electric field intensity