Question

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

Answer 1

Answer:

The answer is "Option A"

Explanation:

Energy stored in capcitor$=\frac{1}{2}\ cv^2$

For point A:

$C_A=\frac{\varepsilon_0 2A}{\frac{d}{2}}=\frac{4\ \varepsilon_0 A}{d}$

For point B:

$C_B=\frac{\varepsilon_0 2A}{2d}=\frac{\varepsilon_0 A}{d}$

For point C:

$C_c=\frac{\varepsilon_0 A}{d}$

For point D:

$C_D=\frac{\varepsilon_0 A}{2 \frac{d}{2}}=\frac{\varepsilon_0 A}{d}$

For point E:  $C_E=\frac{\varepsilon_0 A}{2 \times 2d}=\frac{\varepsilon_0 A}{4d}$

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