Step-by-step explanation:
A.
The capacitance of a capacitor, C is:
C = £° \(A * d)
where,
A = plate area
d = distance between the plate
£° = free space permitivity
In Capacitor 1, plate area A, plate separation, d
C1 = £°\(A * d)
In Capacitor 2, plate area 2A, plate separation d
C2 = £°\(2A * d)
= 2 * C1
In Capacitor 3, plate area A, plate separation 2d
C3 = £°\(A * 2d)
= 1/2 * C1 = 0.5 * C1
So,
C3 < C1 < C2.
B.
The potential difference between two plates on a capacitor is:
V = Q * C
Where,
V = potential difference
Q = charge on the plate
In Capacitor 1, C = C1
Potential difference, V1 = Q * C1
In Capacitor 2: C2 = 2 * C1
Potential difference, V2 = Q * 2C1
= V1 * 2
In Capacitor 3: C3 = 1/2 * C1
Potential difference: V3 = 1/2 * Q * C1
=2 * V1
So,
V2 < V1 < V3.
C.
The electric field magnitude between the plates of a capacitor:
E = V/d
where,
V = the potential difference between the plates
d = distance between the plates
In Capacitor 1, C1; potential difference V1, plate separation d
electric field, E1 = V1/d
In Capacitor 2, C2; potential difference V2 = 1/2 * V1, plate separation d
electric field, E2 = 1/2 * V1/d
= V1/2d
= 1/2 * E1
In Capacitor 3, C3; potential difference 2V1, plate separation 2d
electric field: E3 = 2 * V1/2d
= V1/d = E1
So,
E2 < E1 and E3.
D.
Energy stored in a capacitor is
W = 1/2 * Q * V
In Capacitor 1, C1; potential difference, V1
energy: W1 = 1/2 * Q * V1
In Capacitor 2, C2; potential difference, V2 = 1/2 * V1
energy: W2 = 1/2 * Q/(V1/2)
= 1/2 * W1
In Capacitor 3, C3; potential difference, V3 = 2 * V1
energy: W3 = 1/2 * Q(2 * V1)
=2 * U1
So,
W2 < W1 < W3.
E.
The energy density in a capacitor is:
u = 1/2 * £° * E^2
where,
E is the electric field strength
In Capacitor 1, C1; electric field, E1
Energy density: u1 = 1/2 * £° * E1^2
In Capacitor 2, C2; electric field, E2 = 1/2 * E1
energy density: u2 = 1/2 * £° (E1/2)^2
= 1/4 * E1
In Capacitor 3, C3; electric field E3 = E1
Energy density: u3 = 1/2 * £° * E1^2
So,
u2 < u1 and u3.