The dielectric (breakdown) strength of air is 3.00 times 10^6 V/m, and that of a

Question

The dielectric (breakdown) strength of air is 3.00 times 10^6 V/m, and that of a rubber is 2.27 times 10^7V/m. An air-filled, parallel-plate capacitor Can store no more than 7.00 times 10^-2J of energy before breaking down. Assume that the dielectric constant of the rubber is 8.00 and i aration of the two plates is 1.73 time 10^-4m. (15) What is the inner surface area of one plate? (A) 10.2 m^2; (B) 9.20 m^2; (C) 8.20 m^2; (D) 7.20 m^2; (E) 6.2 m^2. (16) What is the maximum energy that this capacitor can store if it filled with the rubber? (A) 24.1 J; (B) 26.1 J; (C) 28.1 J; (D) 30.1 J; (E) 32.1 J.

Explanation / Answer

For air -

E = 3.0x10^6 V/m

d = 1.73x10^-4 m

So, V = E*d = 3.0x10^6x1.73x10^-4 = 5.19x10^2 Volt

Now,

C = A / d = (8.854E-12 x A) / (1.73x10^-4) = 5.12x10^-8xA

Now, E = 0.5xCxV^2 = 0.5x 5.12x10^-8xAx519^2 = 0.07

=> 0.00689xA = 0.07

=> A = 10.15 m^2

This is nearest to option (A).

So, the correct answer is option (A)

(16) Cr = 8C = 8x5.12x10^-8x10.15 = 4.16x10^-6

and, V = 2.27x10^7x1.73x10^-4 = 3927.1 V

E = 0.5xCrxV^2 = 8x(0.5xCxV^2) = 4x 4.16x10^-6x3927.1^2 = 25.662 J

This is nearest to option (B)

So, option (B) is the correct answer.

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