A double-layer cylindrical capacitor consists of conductors of radii R_(1) and R_(3) and two layers of dielectrics of relative permittivtties epsilon_(1) and espion_(2). The radius of the common surface of the dielectrics. Is R_(2) . The breakdown field strengths of the dielectrics are E_(1) and E_(2) respectively. What is the breakdown voltage of this capacitor if (a) epsilon_(1)R_(1)E_(1) lt epsilon_(2)R_(2)E_(2) (b)epsilon_(2)R_(2)E_(2)gtepsilon_(1)E_(1)R_(1)? [Hint: If E_(1)=E_(1max) and E_(2)gt ,E_(2max) dielectric 1 will break first and if E_(2)=E_(2max') E_(1) gt E_(1max) dielectric 2 will break first.]

A double-layer cylindrical capacitor consists of conductors of radii R

1.	A double-layer cylindrical capacitor consists of conductors of radii R_(1) and R_(3) and two layers of dielectrics of relative permittivtties epsilon_(1) and espion_(2). The radius of the common surface of the dielectrics. Is R_(2) . The breakdown field strengths of the dielectrics are E_(1) and E_(2) respectively. What is the breakdown voltage of this capacitor if (a) epsilon_(1)R_(1)E_(1) lt epsilon_(2)R_(2)E_(2) (b)epsilon_(2)R_(2)E_(2)gtepsilon_(1)E_(1)R_(1)? [Hint: If E_(1)=E_(1max) and E_(2)gt ,E_(2max) dielectric 1 will break first and if E_(2)=E_(2max') E_(1) gt E_(1max) dielectric 2 will break first.]
Answer» Answer :(a)`V_(BREAK)=E_(1)R_(1)(In(R_(2))/(R_(1))+(epsilon_(1))/(epsilon_(2))In(R_(3))/(R_(2)))` (B)`V_(break)=E_(2)R_(2)((epsilon_(2))/(epsilon_(1))In(R_(2))/(R_(1))+In(R_(3))/(R_(2)))`

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