A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates. A sheet having thickness ((1)/(3))^ rd of the separation between the plates and relative permittivity K is introduced

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Correct answer: C. (3 K C)/(2 K+1)

Original capacitance: C = ( _0 A)/(d) After inserting dielectric of thickness (d)/(3) , system becomes two capacitors in series. Vacuum region: C_1 = ( _0 A)/(2d/3) = (3C)/(2) Dielectric region: C_2 = (K _0 A)/(d/3) = 3KC Equivalent capacitance: 1 C_ new = (1)/(C_1) + (1)/(C_2) = (2)/(3C) + (1)/(3KC) = (2K+1)/(3KC) C_ new = (3KC)/(2K+1)

A parallel plate capacitor has capacitance C , when there is vacuum...

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