A vacuum-insulated parallel-plate capacitor with plate separation d has capacitance C0.
What is the capacitance if an insulator with dielectric constant κ and thickness d/2 is slipped between the electrodes? Assume plate separation is unchanged.
Express your answer in terms of the variables d, C0, and κ.
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we assume…it is two capacitors in series ….one separation is d /2 with dielectric constant k and the other …separation d/2 and vacuum…
for half separation and vacuum…2Co
for half separation and dielectric constant k….2kCo
they are series…so 2Co x 2kCo / ( 2Co +2kCo)
C = Co x2 k / ( 1+k )
checking formula….if k = 1 >>> C= Co
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