four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same

Question

four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitors A and C are separated by a distance d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dielectrics with constant ? = 5.
List the capacitors in order of increasing capacitance. Which one has the greatest potential difference between its plates? Which one stores the greatest amount of electrical potential energy?

Explanation / Answer

Capacitance = eps*A/d where eps= permittivity of medium so, C(A) = capacitance of A = (eps0)*A/d C(B)= (eps0)*A/(2d) C(C)=(5eps0)*A/d C(D)=(5eps0)/(2d) so, C(C)>C(D)>C(A)>C(B) potential difference = q/C, so minimum Capacitance gives max potential difference so, B has max potential difference. energy stored = (q^2)/(2C) so, again minimum capacitance gives maximum energy stored or, capaictor B has max energy stored.

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