We performed capacitance measurements between silver layers on the back side of thin (<1 mu m) mica substrates in surface force apparatus to determine the contact area with very high precision (<0.1% of the total area) and at a rate that is faster (similar to 1 kHz) than that in more traditional methods based on interferometry. To demonstrate the capabilities of the technique, we measured the adhesion and adhesion hysteresis between two mica surfaces. A peculiar discontinuous decrease in contact area, with decreasing load, between two dry mica surfaces is observed. We also studied the possible effect of shear forces on the value of the contact area due to adhesive forces, as in JKR theory.