The capacity of a parallel plate condenser is a measure of its ability to store charge. It is directly proportional to the area of the plates and inversely proportional to the distance of separation between the plates.

Option 1 states that doubling the areas of the plates and doubling both the areas of the plates and the distance of separation between them will double the capacity of the condenser. This is incorrect. Doubling the areas of the plates will indeed double the capacity, but doubling both the areas of the plates and the distance of separation between them will not double the capacity. Therefore, option 1 is incorrect.

Option 2 states that doubling the areas of the plates and reducing the distance of separation between the plates to half the original separation will double the capacity of the condenser. This is correct. Doubling the areas of the plates will double the capacity, and reducing the distance of separation to half will also double the capacity. Therefore, option 2 is correct.

Option 3 states that reducing the distance of separation between the plates to half the original separation will double the capacity of the condenser. This is incorrect. Reducing the distance of separation will increase the capacity, but it will not double it. Therefore, option 3 is incorrect.

Option 4 states that