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Anni [7]
4 years ago
5

A certain dielectric with a dielectric constant = 24 can withstand an electric field of 4 107 V/m. Suppose we want to use this d

ielectric to construct a 0.89 µF capacitor that can withstand a potential difference of 1930 V. (a) What is the minimum plate separation? (b) What must the area of the plates be?
Physics
2 answers:
mr_godi [17]4 years ago
8 0

Answer:

Explanation:

Electric field E = 4 x 10⁷ V / m

Dielectric constant k = 24

capacitance of capacitor

C = kε₀ A / d

d = plate separation

A =  plate area

C = .89 x 10⁻⁶

V / d = electric field

for minimum d , electric field will be maximum

V / d  = 4 x 10⁷

1930 / d = 4 x 10⁷

d = 1930 / 4 x 10⁷

d = 482.5 x 10⁻⁷ m

= 48.25 x 10⁻⁶ m

C = kε₀ A / d

.89 x 10⁻⁶ = 24 ε₀ A / d

A = .89 x 10⁻⁶  X d /  24 ε₀

A = .89 x 10⁻⁶  X 48.25 x 10⁻⁶  /  24  x 8.85 x 10⁻¹²

= 42.9 / 212.4

= .2019 m²

dsp734 years ago
4 0

Answer:

a) d=0.4699\,m

b) A=1969.1\,m^2

Explanation:

Given that:

dielectric constant, k=24

electric field, E=4107 \,V.m^{-1}

capacitance, C=0.89\times 10^{-6}\,F

potential difference, V=1930\,V

(a)

We know for two parallel plates is given by:

V=E.d

where: d= distance between the plates.

1930=4107\times d

d=0.4699\,m

(b)

For parallel plate capacitor we have:

C=\frac{k.\epsilon_0.A}{d}

where:

A= area of plates

permittivity of free space, \epsilon_0=8.85\times 10^{-12}\,F.m^{-1}

0.89\times 10^{-6}=\frac{24\times 8.85\times 10^{-12}\times A}{0.4699}

A=1969.1\,m^2

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