"A 400 kV cable requires less insulation than a 240V cable."
This was regarded as False in one of my question papers, but why? Doesn't a higher voltage means, lower current(P=V. I) and a lower voltage means higher current which brings us to P=I2.R | Therefore the higher the current, the more power is lost as heat, and shouldn't this mean the 240V cable needs to be insulated more?
Current has nothing to do with it, it is the voltage (potential difference) across the insulation which is important.
If you are worried about current it is the heating effect of the current which is important and you want to either produce less of a heating effect or allow the heat to escape easily from the conductor.
Insulators have a dielectric strength or breakdown potential gradient which is the maximum electric field strength that can be sustained within the material before it ceases to be an insulator and becomes a conductor. For example for air it is $3\,\rm MV\, m^{-1}$ and for plastics it can range from $20\,\rm MV\, m^{-1}$ to $200\,\rm MV\, m^{-1}$.
What this means is that if the voltage (potential difference) across an insulator is too high the material becomes a conductor.
So A 400 kV cable requires more insulation than a 240V cable.
You may think that an overhead power line has no insulation but it does air around it and is suspended from a substantial line of insulators as shown below.
As Farcher has already pointed out, electrical insulation requirements have has nothing to current. The ampacity (size) of the conductors themselves, however, needs to be sufficient to prevent overheating when carrying normal load current.
That being said, the statement "A 400 kV cable requires less insulation than a 240V cable" needs to be qualified.
First, you need to recognize that electrical insulation can be a solid insulating material, some liquids (e.g. oils), and gases including air. It is usually a combination of solid insulating material (polymers, ceramics, or other inorganic materials) and air. If you take into account the total insulation needed, then the answer is 400 kV cable requires more insulation than a 240 V cable.
Now, if the statement were “A 400 kV cable may require less solid insulation than a 240 V cable”, that statement might be true if we are talking about high voltage cables located high off the ground, since air is the primary insulation for such cables. 240-volt cables can come into direct contact with grounded objects, so that air cannot be relied upon for electrical insulation to ground. You are relying totally on solid insulation around the conductors. What’s more such cables may be subjected to physical abuse (in contrast to the HV cables that are “protected” by virtue of their inaccessibility) and are therefore typically jacketed to protect the insulated conductors within from physical damage.
Take a close look at the photo Farcher provided. The tower is fixed to the ground but needs to support the HV cables. Good quality solid insulation is needed for the support to prevent dielectric breakdown through the support between the cables and the tower, as well as prevent electrical tracking over the surface of the support. The material for the support shown is probably made of some inorganic insulation (e.g, ceramic), which is both a good insulator and resistant to electrical tracking over the surface of the material. Note also the shape of the support. It is provided with a series of, for want of a better term, discs. This effectively increases the distance over the surface of the insulation between the cables and the tower, making it more resistant to electrical tracking over the surface, than it would be if it were, say, simply a smooth cylindrical rod.
Hope this helps.
