A vacuum-insulated parallel-plate capacitor with plate separation d has capacita

Question

A vacuum-insulated parallel-plate capacitor with plate separation d has capacitance C0.

Part A

What is the capacitance if an insulator with dielectric constant 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 .

A vacuum-insulated parallel-plate capacitor with plate separation d has capacitance C0.

Part A

What is the capacitance if an insulator with dielectric constant 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 .

Explanation / Answer

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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