Question

You have three parallel plate capacitors, each consisting of two parallel disks of metal separated by a gap filled with some material. Rank the capacitors by their capacitances from highest to lowest, based on the provided plate radii (r), plate separations (d), and filler materials.
Capacitor 1 r=5.77 mm, d=54.6 um filled with paper (k value 3.50)
Capacitor 2 r=8.87 mm, d=36.7 um, filled with porcelain (k value 7.00)
Capacitor 3 r=14.3 mm, d=12.4 um, filled with Germanium (k value 16.0)

Answer 1

Concepts and reason

The concept used to solve this problem is the capacitance of the parallel plate capacitor.

First, use the relation between area, dielectric constant, and distance to find the capacitance of three capacitors.

Finally, Rank the capacitors from their value from highest to lowest.

Fundamentals

The expression for the capacitance of the parallel plate capacitor is,

…… (I)

Here, is the permittivity of space, A is the area of the disk, d is the distance between the two capacitors; k is the relative permittivity and is the capacitance of the parallel plate.

The expression for the area of the disk is,

Here, r is the radius of the disk.

Use for A in the equation (I),

The expression for the capacitance of the parallel plate capacitor filled with paper at is,

Here, is the capacitance at plates filled with paper and k is the relative permittivity of paper.

Substitute for , for k, for r and for d.

The capacitance of the parallel plate capacitor filled with paper at is.

The expression for the capacitance of the parallel plate capacitor filled with porcelain at is,

Here, is the capacitance at plates filled with porcelain and k is the relative permittivity of porcelain.

Substitute for , for k, for r and for d.

The expression for the capacitance of the parallel plate capacitor filled with germanium at is,

Here, is the capacitance at plates filled with Germanium and k is the relative permittivity of Germanium.

Substitute for , for k, for r and for d.

When comparing the capacitance value of three capacitors, the capacitor has more value when compared with and .The second most large is the when compared with.

Ans:

The Rank of the capacitors from highest to lowest is .