  We start from microscopic approach to many body physics and show the
analytical steps and approximations required to arrive at the concept of
quantum capacitance. These approximations are valid only in the semi-classical
limit and the quantum capacitance in that case is determined by Lindhard
function. The effective capacitance is the geometrical capacitance and the
quantum capacitance in series, and this too is established starting from a
microscopic theory.
