The plate areas and plate separations of five parallel plate capacitors are Rank these according to their capacitances, least to greatest.
A)1, 2, 3, 4, 5
B)5, 4, 3, 2, 1
C)5, then 3 and 4 tie, then 1, then 2
D)4, then 1 and 2 tie, then 5, then 3
E)3, then 5, then 1 and 2 tie, then 4

Question

The plate areas and plate separations of five parallel plate capacitors are  Rank these according to their capacitances, least to greatest.
A)1, 2, 3, 4, 5 
B)5, 4, 3, 2, 1 
C)5, then 3 and 4 tie, then 1, then 2 
D)4, then 1 and 2 tie, then 5, then 3 
E)3, then 5, then 1 and 2 tie, then 4

Quizplus · Accepted Answer

The capacitance of a parallel plate capacitor is given by C = εA/d, where ε is the permittivity of the dielectric material between the plates, A is the area of each plate, and d is the distance between the plates. 
Ranking the capacitors by capacitance, we need to compare their plate areas and plate separations. 
Considering only the plate areas, larger plate areas lead to larger capacitances. 
Considering only the plate separations, smaller plate separations lead to larger capacitances. 
Therefore, the capacitors with the largest plate area and smallest plate separation will have the largest capacitance. 
Ranking the given capacitors from smallest to largest capacitance: 
Capacitor 4 has the smallest plate area and largest plate separation, so it has the smallest capacitance. 
Capacitors 1 and 2 both have the same plate area and plate separation, so they have the same capacitance, which is larger than that of capacitor 4. 
Capacitor 5 has the largest plate area and smallest plate separation, so it has the largest capacitance. 
Capacitor 3 also has a large plate area, but its plate separation is larger than that of capacitors 1 and 2, so it has a smaller capacitance than they do. 
Therefore, the ranking is: 4, 1 and 2, 3, 5. 
The only choice that matches this ranking is D.

The Plate Areas and Plate Separations of Five Parallel Plate