If particle size halves theoretical plates doubles (assuming column length remains the same) . If particle size halves back pressure increases by a factor of four.
If column length doubles theoretical plates doubles. If column column length doubles, analysis time doubles. As column length increases back pressure increases linearly.
Here is an example of applying this information in column selection:
A 200 mm long column packed with 10um particles generates about 6000 theoretical plates, an order of column efficiency that provides adequate separation in many cases. By reducing the particle size from 10um to 5um the efficiency of the same 200-mm column is doubled to about 12000 theoretical plates. However, this column generates a back pressure that is four times that of the one filled with 10um particles. Very often an efficiency of 12000 plates is not required, so the column length can be halved to 100mm, resulting in an efficiency of 6000 plates, and at the same time halving analysis time; the back pressure is only a factor two greater than the 200mm column with 10um particles