Voltage Breakdown Equation - Discrepancy in Logic

Hello everyone,

I had a question regarding a voltage breakdown equation that I saw in a book. It helped me to try and solve question 10 in the "Conductors and Insulators" worksheet linked here http://www.allaboutcircuits.com/worksheets/candi.html. Here is the equation:

Vmax = Emax * d

Where,
d = thickness of insulator
Emax = dielectric strength of insulating material
Vmax = breakdown voltage

It's more of a clarification then anything else, I was wondering if the dielectric strength is to remain constant, then increasing the thickness of the material would increase the breakdown voltage due to proportionality, however, doesn't increasing the thickness of a material reduce its electrical resistance? Or is that only for conductors?

I looked on the forum and couldn't find anything specific, mostly on lightening, zener/diode voltage breakdown, and transistor voltage breakdown.

If anyone could make this clarification, I would appreciate it. Thank you.

Jake1234 said:

doesn't increasing the thickness of a material reduce its electrical resistance?

Click to expand...

Suppose you have a 1 cm cube of a material. Define an axis that is perpendicular to one of the cube's faces the axis to measure the resistance along (touch your ohmmeter probes to the two surfaces perpendicular to this axis). OK, now double the "thickness" along that axis and measure the resistance again. Will it be larger or smaller than the first resistance?

Well, I was thinking along the lines of an I vs. V curve. I know that increasing the thickness of a material, reduces it's electrical resistance because more current would flow through the device due to the larger cross sectional area.

However, in the case of voltage breakdown, a thicker material would provide less resistance, therefore allowing more current to flow. So wouldn't that mean a lesser voltage would be required for breakdown to occur if more current is allowed to flow through the insulating material?

I'm trying to think in terms of the mathematics here... I know V = IR and I could look at it this way and say with the increase in cross-sectional area, a less resistance would result constituting more current flow. With more current flow, a higher voltage would be needed. But, most devices that have voltage breakdown aren't linear devices so they don't obey Ohms law...

When dealing with an insulator, current is the result of a failure. Ohm's law doesn't apply. Thicker insulation = more insulation. The thicker the insulation, the more voltage it will withstand.

I think this discussion is confusing adding resistive material in series (insulation thickness) where the resulting resistance increases, versus adding resistive material in parallel (more cross-sectional area through which current can flow) where the resulting resistance decreases.

I think it's more clearer now. Since Ohm's law doesn't apply, then the more insulation will result in more impedance which makes intuitive sense.

Thank you someonesdad, beenthere, and davebee for your clarification.