Electrostatics Basic Question Why ,if we increase the charge on a conductor its potential also increases?
That is, Q directly proportional to V.
Why ,if an insulated conductor is given some charge it acquires a certain potential?
 A: In this case it is more accurate to say that V is proportional to Q because the potential, V, (at some distance from the charged insulator) is dependent on how much charge, Q there is on the charged insulator setting up the electric field.
It is not the source (charged insulator) that acquires potential--the potential we are referring to is at a point away from the source that a hypothetical second charge that would stand to gain electric potential energy at, if placed there.
A: V is energy per coulomb, or in other units, energy per electron. Here energy is potential energy that comes from pushing electrons near other electrons against an electrostatic force. 
Usually V is the potential difference between two points. Potential arises from a set of charges, typically a charged object. The charges fill space with an E field. V is change in potential energy of a test charge that arises from moving with or against the force from the E field. 
When we talk about the potential of a conductor, we mean the potential difference where one point is at infinity, and the other is on the surface of the conductor. So V is the energy needed to add one more electron to the conductor. Note that it doesn't matter which infinitely distant point we choose. Nor does it matter which point on the surface. Charges on a conductor will move so that no electron has more potential energy than the others. So the potential is the same everywhere on the surface. 
Another way to think about this is that if you add more electrons to a charged object, it gets more crowded. The electrons must get closer together. This increases the potential energy of each electron. So when Q goes up, so does V. 
This also explains why the potential goes up when the charged object shrinks. 
