Question

Four plates of equal area A are separated by equal distance d and are arranged as shown in Figure A. Their equivalent capacity is C₁. Then, the same four plates are arranged as shown in Figure B, and their equivalent capacity is C₂, then C₁ : C₂ is ______.

Fig. A	Fig. B

Options

• 3 : 4

• 2 : 3

• 3 : 2

• 4 : 3

Answer 1

Four plates of equal area A are separated by equal distance d and are arranged as shown in Figure A. Their equivalent capacity is C₁. Then, the same four plates are arranged as shown in Figure B, and their equivalent capacity is C₂, then C₁ : C₂ is 2 : 3.

Explanation:

Let X(1, 4) be a positive plate and Y(2, 3) be a negative plate.

The equivalent capacitance is just a parallel combination of two capacitors, therefore,

`C_1 = (ε_0A)/d + (ε_0A)/d = (2ε_0A)/d`

Now,

the equivalent capacitance is just a parallel combination of three capacitors. Therefore,

`C_2 = (ε_0A)/d + (ε_0A)/d + (ε_0A)/d = (3ε_0A)/d`

Therefore, `C_1/C_2 = 2/3`