Three parallel-plate capacitors each store the same amount of charge. capacitor 1 has a plate area aand a plate separation d. capacitor 2 has a plate area 2a and a plate separation d. capacitor 3 has a plate area a and a plate separation 2d.

part a
rank the three capacitors, based on their capacitance.
part b
rank the three capacitors, based on the potential difference between the plates.
part c
rank the three capacitors, based on the electric field magnitude between the plates.
part d
rank the three capacitors, based on the energy stored.
part e
rank the three capacitors, based on the energy density.

A)

The capacitance of a parallel-plate capacitor is given by

where

A is the plate area

d is the plate separation

Here we have:

- Capacitor 1: plate area A, plate separation d

capacitance:

- Capacitor 2: plate area 2A, plate separation d

capacitance:

- Capacitor 3: plate area A, plate separation 2d

capacitance:

So ranking the three capacitor from least to greatest capacitance we have:

2.

The three capacitors have same amont of charge, Q.

The potential difference between the plates on each capacitor is given by

so here we have

- Capacitor 1:

Potential difference:

- Capacitor 2:

Potential difference:

- Capacitor 3:

Potential difference:

So ranking the three capacitor from least to greatest potential difference we have:

C.

The electric field magnitude between the plates of a capacitor is given by

where V is the potential difference between the plates and d is the plate separation

So here we have

- Capacitor 1: potential difference , plate separation d

electric field:

- Capacitor 2: potential difference , plate separation d

electric field:

- Capacitor 3: potential difference , plate separation 2d

electric field:

So ranking the three capacitor from least to greatest electric field we have:

D.

The energy stored in a capacitor is

where Q is the same for the three capacitors

Here we have

- Capacitor 1: potential difference

energy:

- Capacitor 2: potential difference

energy:

- Capacitor 3: potential difference

energy:

So ranking the three capacitor from least to greatest energy we have:

E.

The energy density in a capacitor is given by

where E is the electric field strength

Here we have

- Capacitor 1: electric field

Energy density:

- Capacitor 2: electric field

energy density:

- Capacitor 3: electric field

Energy density:

So ranking the three capacitor from least to greatest energy density we have:

b

explanation:

ill do it for 100, also this isnt 80 its 40