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: