a) In order to increase the maximum operating voltage of a paralle-plate capacitor we can insert a dielectric with higher "\\kappa" (dielectric constant) between its plates to weak the electric field between the capacitor's plates and to avoid the breakdown of the capacitor electrically.
b) There are two important factors: dielectric material and the distance between the plates. The dielectric material with high dielectric constant helps us to avoid the breakdown of the capacitor electrically, the small distance between the plates helps us to design the capacitor with a small size and large capacitance.
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