Suppose several different parallel-plate capacitors are charged up by a constant-voltage source. Thinking of the actual movement and position of the charges on an atomic level, why does it make sense that the capacitances are proportional to the surface areas of the plates? Why does it make sense that the capacitances are ?inversely? proportional to the distance between the plates?

Solution 2DQ By definition, capacitance is the ability of a conductor to store energy in the form of electric charges. Mathematically, capacitance of a parallel plate capacitor is given as A C = d0 . Therefore, capacitance is directly proportional to the area of a plate and d is the distance between the plates. Now, the conductor will be able to hold more electrical charges if the plates have large area. This would increase the capacitance of the conductor. Therefore, the capacitance has to be proportional to the surface areas of the plates. If the distance between the capacitor plates is high, the work done to move the charges between the plates would increase. Work done is directly proportional to potential difference as W = qV , where q is the charge, W is the work done and V is the potential difference. . But potential difference itself is inversely related to capacitance as C = Q/V , where Q is the charge. Therefore, an increase in potential difference would result in the decrease of capacitance. To avoid this, the separation between the capacitor plates have to be low so that high value of capacitance can be maintained. Therefore, capacitance has to be inversely proportional to the distance between the plates.;