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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.
C=?

Sagot :

The capacitance if an insulator with dielectric constant κ and thickness d/2 is slipped between the electrodes C = 2K∉A/d

Let A represent the cross-sectional area of the electrodes.

Let C stand for capacitance.

The electric field between the electrodes is denoted by E.

Be the charge per unit area, sigma.

be the permittivity of empty space, and K is assumed to be an insulator's dielectric constant in the question.

It is inserted between the electrodes as d/2.

the current electric field between electrodes.

E equals sigma /2 plus sigma /2.

E = sigma/ ——— As we are aware, E = V /(d/2)

V=E d/2 V=sigma /*d/2

V = dsigma/2 ——— Once more, we are aware of 2.

C = Q/V

C is equal to sigma A/(sigma d/2) Q = sigma A (from equation 2

For an insulator with a dielectric constant of K, C = 2A/d.

C = 2K∉A/d

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