# Parallel-plate capacitor – problems and solutions

1. A parallel-plate capacitor has initial capacity C, the permittivity of free space is ε_{o}, 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 5ε_{o}, what is the final capacity of the parallel-plate capacitor.

__Known :__

The capacity of capacitor = C

The permittivity of free space = ε_{o}

Plate area = A

The distance between plates = d

__Wanted:__ Capacity of the capacitor (C)

__Solution :__

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

__Solution :__

**The formula of the parallel-plate capacitor :**

**The capacity of capacitors :**

The capacitor that has the largest capacity is capacitor C_{3.}

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…

__Known :__

**Capacitor 1 :**

Surface area = 2A

The distance between plates = d_{1}

**Capacitor 2 :**

Surface area = A

The distance between plates = 2 d_{1}

Wanted: The capacity comparison of the capacitor 1 and 2

__Solution :__

5.

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

__Solution :__

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

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

If A_{1 }= ½ A_{2} and d_{2} = 3 d_{1 }then determine the ratio of capacities of the parallel-plate capacitor between the image 2 and the image 1.

__Known :__

Parallel-plate capacitor I :

A_{1} = 1

d_{1} = 1

Parallel-plate capacitor II :

A_{2} = 2

d_{2} = 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 II :

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