A parallel-plate capacitor is constructed from a layer of silicon dioxide of thi

Question

A parallel-plate capacitor is constructed from a layer of silicon dioxide of thickness 1.4 × 105 m between two conducting films. The dielectric constant of silicon dioxide is 3.8 and

its dielectric strength is 8 × 106 V/m.
The permittivity of free space is 8.85 ×

1012 C2/N · m2.

What voltage can be applied across this capacitor without dielectric breakdown?

Answer in units of V.

1b.

What should the surface area of the layer of silicon dioxide be for a 12 pF capacitor?

Answer in units of mm2.

1c.

Estimate the number of these capacitors that can fit into a square 2 cm by 2 cm.

Explanation / Answer

part a:

voltage that can be applied safely=dielectric strength*distance between plates

=8*10^6*1.4*10^(-5)=112 volts

part b:

capacitance=epsilon*dielectric constant*area/distance between plates

==>area=capacitance*distance/(epsilon*dielectric constant)

=12*10^(-12)*1.4*10^(-5)/(8.85*10^(-12)*3.8)

=5*10^(-6) m^2

=5 mm^2

part c:

total area of the square=0.02*0.02 m^2

=4*10^(-4) m^2

then number of capacitors =4*10^(-4)/(5*10^(-6))

=80

so 80 of these capacitors can fit into a square of 2 cm by 2 cm

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