Parallel-plate capacitor – problems and solutions

1. A parallel-plate capacitor has initial capacity C, the permittivity of free space is εo, plate area is A, the distance between plates is d. If the plate area increased by 4 times, the distance between plates becomes 2d and the permittivity of free space is 5εo, what is the final capacity of the parallel-plate capacitor.

Known :

The capacity of capacitor = C

The permittivity of free space = εo

Plate area = A

The distance between plates = d

Wanted: Capacity of the capacitor (C)

Solution :

Parallel-plate capacitor – problems and solutions 1

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2. The capacitor that has the largest capacity based on the graphic below is

Parallel-plate capacitor – problems and solutions 2

Solution :

The formula of the parallel-plate capacitor :

Parallel-plate capacitor – problems and solutions 3

The capacity of capacitors :

Parallel-plate capacitor – problems and solutions 4

The capacitor that has the largest capacity is capacitor C3.

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3.

Consider the following factors!
(1) Dielectric constant
(2) The potential difference between the plates
(3)
Plate thick
(4) The surface area of the plate
(5) The distance between the plates
(6) Amount of electric charge
Factors affecting the capacities of parallel plate capacitors are …

Solution :

(1), (4) and (5)

4. The capacity comparison of the capacitor 1 and 2 is…

Parallel-plate capacitor – problems and solutions 5Known :

Capacitor 1 :

Surface area = 2A

The distance between plates = d1

Capacitor 2 :

Surface area = A

The distance between plates = 2 d1

Wanted: The capacity comparison of the capacitor 1 and 2

Solution :

Parallel-plate capacitor – problems and solutions 6

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5.

Parallel-plate capacitor – problems and solutions 15

Determine comparison of the capacity of Parallel-plate capacitor I and II.

Solution :

Parallel-plate capacitor – problems and solutions 16

Comparison of the capacity of Parallel-plate capacitor I and II :

Parallel-plate capacitor – problems and solutions 17

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6. Two parallel-plate capacitors shown in the figure below.

If A1 = ½ A2 and d2 = 3 d1 then determine the ratio of capacities of the parallel-plate capacitor between the image 2 and the image 1.

Parallel-plate capacitor – problems and solutions 18

Known :

Parallel-plate capacitor I :

A1 = 1

d1 = 1

Parallel-plate capacitor II :

A2 = 2

d2 = 3

Wanted: the ratio of capacities of the parallel-plate capacitor between the image 2 and the image 1

Solution :

Parallel-plate capacitor I :

Parallel-plate capacitor – problems and solutions 19

Parallel-plate capacitor II :

The ratio of capacities of the parallel-plate capacitor II and I :

Parallel-plate capacitor – problems and solutions 20