Five air-filled parallel-plate capacitors have the plate areas and plate separations listed below, where A and d are constants. The capacitors are each connected to the same potential difference. Which capacitor stores the greatest amount of energy?

a.
Area: 2A
Separation : d/2
b.
Area: 2A
Separation : 2d
c.
Area: A
Separation : d
d.
Area: A/2
Separation : d/2
e.
Area: A/2
Separation : 2d

Respuesta :

Answer:

The answer is "Option A"

Explanation:

Energy stored in capcitor[tex]=\frac{1}{2}\ cv^2[/tex]

For point A:

[tex]C_A=\frac{\varepsilon_0 2A}{\frac{d}{2}}=\frac{4\ \varepsilon_0 A}{d}\\\\[/tex]

For point B:

[tex]C_B=\frac{\varepsilon_0 2A}{2d}=\frac{\varepsilon_0 A}{d}\\\\[/tex]

For point C:

[tex]C_c=\frac{\varepsilon_0 A}{d}\\\\[/tex]

For point D:

[tex]C_D=\frac{\varepsilon_0 A}{2 \frac{d}{2}}=\frac{\varepsilon_0 A}{d}\\\\[/tex]

For point E:  [tex]C_E=\frac{\varepsilon_0 A}{2 \times 2d}=\frac{\varepsilon_0 A}{4d}\\\\[/tex]

therefore C_A has the maximum capacitance and max energy same energy is dir proportional to C for the same J