Question

Smarty McGuy intends to charge the parallel plate capacitor inside his intergalactic Ford Pinto (built by Doc Dre) with a lightning strike of 26x10³ amps. Doc Dre's capacitor specifications are listed below:

The distance between the capacitor plates is 5 microns

The surface area of the capacitor plates is 3,844 cm²

There is a dielectric between the capacitor plates

What is the minimum dielectric constant of the material between the plates needed to store all the charge from the lightning assuming that the lightning strike lasts for 6x10^-6 seconds and provides 1.21 Gigawatts of power? Assume the dielectric doesn't reach its breakdown voltage.

Answer 1

Let us first calculate the voltage output required for 1.21 GW of power.

The lightning lasts for 6 microseconds.

So, energy produced is

Now, each lightning strike carries a current of about

The lightning lasts for 6 microseconds.

So, charge that needs to be stored is

Voltage produced due to this power output is

So, capacitance of the capacitor required is

If this capacitor has a surface area A, distance between two plates is d then

k is the dielectric constant of the medium, is the permittivity of free space.

It is given that

Putting the values,

This is the value of the dielectric constant of the material that is placed in between the capacitors.