Parallel Plate Capacitor With Multiple Plates

       In case of electronic apparatus, in many cases, a multiple plate capacitor is used. This is shown with terminals A and B in the Fig. 1. All the metal plates from capacitance with the adjacent plate.

      In such capacitor, one set of plates is fixed while other is movable. The set of moving plates can be moved in and out of the space between the fixed plates, without touching them. The alternate plates are connected to the terminals A and B.
      Consider such a capacitor with three plates as shown in the Fig. 2.

       It can be seen that there exists two capacitors C1 and C2 between the adjacent plates. Let A be the area of one side of each plate, d b the thickness of the medium between the plates and εr is the relative permittivity of the medium. Hence, according to the capacitance of a parallel plate capacitor,

      Now, as the parameters εr, A and d are same for any combination of plates,
                  C1 = C2
      The two capacitors are in parallel,

       Now, if the n plates are used, we can write that



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