Question 19.8: Design of a Multi-Layer Capacitor A multi-layer capacitor is......
Design of a Multi-Layer Capacitor
A multi-layer capacitor is to be designed using a BaTiO_{3} formulation containing SrTiO_{3}. The dielectric constant of the material is 3000. (a) Calculate the capacitance of a multi-layer capacitor consisting of 100 layers connected in parallel using nickel electrodes. The area of each layer is 10 mm × 5 mm, and the thickness of each layer is 10 μm.
(a) The capacitance of a parallel plate capacitor is given by
C = \frac{kε_{0}A}{t}
Thus, the capacitance per layer will be
C_{layer} = \frac{(3000)(8.85 × 10^{-12} \ F/m)(10 × 10^{-3} \ m)(5 × 10^{-3} \ m)}{10 × 10^{-6} \ m}
C_{layer} = 13.28 × 10^{-8}
We have 100 layers connected in parallel. Capacitances add in this arrangement. All layers have the same geometric dimensions in this case.
C_{total} = (number of layers) ⋅ (capacitance per layer)
C_{total}= (100)(13.28 × 10^{-8} \ F) = 13.28 \ μF