Question

In the 2001 film The Core, there is a scene in which lightning relentlessly pummels Rome, destroying Il Vittoriano, a famous landmark (pictured below). Il Vittoriano, like most grand buildings in Rome, is made of marble, which has a resistivity of ? = 1.0 ⋅ 108 Ω ⋅ ?. The pictured face of this building features twelve columns (excluding the columns in the wings), each having a height of 14.5 ? and a diameter of 1.5 ? (you can take them to be perfect cylinders).

1. What is the resistance of one such column?

2. These columns stand in parallel and are probably connected directly be rebar, which has such a low comparative resistivity that we will treat it as a perfect conductor. This means that the twelve columns stand in parallel with no other electrically resistive material complicating things. In the film, lightning strikes this set of columns and they explode. A single lightning has an average relative voltage of 1 ?? and generally has a duration of about 0.20 ???. How much energy is delivered to each column to make it explode?

Answer 1

Resistance corresponding to an object of length l and radius r is given by

rho is the resistivity of the object

Putting the values,

Now, power generated on each resistance R when a voltage V is applied across it is

I is the curent through each coloumn

Now, 12 such resistance stand in parallel but they are connected by a single rebar. This means they are in series

So, equivalent resistance is

So, current through each when a voltage of 1 GV is applied is

So, power dissipated across each column is

Hence, energy delivered to each coloumn is