2.33 A parallel plate capacitor is to be designed with a voltage rating 1 kV, using a material of dielectric constant 3 and dielectric strength about 107 Vm–1. (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionisation.) For safety, we should

like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?

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    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    2.33 Potential rating of the capacitor, V = 1 kV = 1000 V

    Dielectric constant of a material, ?r = 3

    Dielectric strength = 107 V/m

    For safety, the field intensity should not cross 10% of the dielectric strength, hence

    Electric field intensity, E = 10 % of 107 = 106 V/m

    Capacitance of the parallel plate capacitor, C = 50 pF = 50 ×10-12 F

    Distance between the plates, d is given by d = VE = 1000106 m = 10-3 m

    Capacitance is given by the relation

    C = ε0?rAd , where ε0 = permittivity of free space = 8.854 ×10-12 C2N-1 m-2

    50 ×10-12 = 8.854×10-12×3×A10-3

    A = 1.88 ×10-3 m2 = 18.8 cm2

    Hence, t

    ...more

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