Which of the following parallel-plate capacitors hold the largest charge?

A) A capacitor with area A and separation 2d connected to voltage 4V
B) A capacitor with area 2A and separation d connected to voltage 2V
C) A capacitor with area 2A and separation 2d connected to voltage V
D) A capacitor with area A and separation d connected to voltage V

C=q/U

C=εε₀A/d
q=CU= εε₀AU/d
A) q1= εε₀A4V/2d= 2 εε₀AV/d
B) q2 = εε₀2A2V/d= 4 εε₀AV/d max
C) q3 = εε₀2A V/2d= εε₀AV/d
D) q4 = εε₀A V/d= εε₀AV/d

To determine which of the parallel-plate capacitors holds the largest charge, we need to use the formula for the capacitance of a parallel-plate capacitor:

C = ε₀ * (A / d)

Where C is the capacitance, ε₀ is the vacuum permittivity (a constant), A is the area of the plates, and d is the separation between the plates.

Assuming the capacitors are identical in terms of material and plate dimensions, the one with the highest capacitance will hold the largest charge.

Let's calculate the capacitance for each option:

A) Capacitor with area A and separation 2d connected to voltage 4V:
C₁ = ε₀ * (A / (2d))

B) Capacitor with area 2A and separation d connected to voltage 2V:
C₂ = ε₀ * ((2A) / d)

C) Capacitor with area 2A and separation 2d connected to voltage V:
C₃ = ε₀ * ((2A) / (2d))

D) Capacitor with area A and separation d connected to voltage V:
C₄ = ε₀ * (A / d)

Now, to compare these capacitances, we must simplify the expressions. We can see that the capacitances C₁ and C₄ are the same as C₃, but the voltages are different.

Let's simplify C₁ and C₂ expressions:

C₁ = ε₀ * (A / (2d))
C₂ = ε₀ * ((2A) / d)

Simplifying C₁:
C₁ = ε₀ * (A / (2d))
= 0.5 * ε₀ * (2A / d)
= 0.5 * C₄

Simplifying C₂:
C₂ = ε₀ * ((2A) / d)
= 2 * ε₀ * (A / d)
= 2 * C₄

So, we can compare the capacitances as follows:

C₁ = 0.5 * C₄ (Option A)
C₂ = 2 * C₄ (Option B)
C₃ = C₄ (Option C)
C₄ = C₄ (Option D)

From this comparison, we can see that Option B has the highest capacitance (2 * C₄). Therefore, the parallel-plate capacitor in Option B holds the largest charge.