Question

If the equivalent capacitance between points A and B of the combination of capacitors shown in figure, is 6C, the capacitor \(C^1\) is

• A. \(9C\)
• B. \(15C\)
• C. \(18C\)
• D. \(24C\)

Hint:

Find each capacitance with epsilon A over d and add them for a parallel connection.

Answer 1

The Correct Option is C

Step 1: Take a common factor:
Let $C_0 = \frac{\varepsilon_0A}{d}$. Half the area halves the capacitance; doubling the gap halves it again.

Step 2: Add:
$C_1 = \frac{C_0}{2}$, $C_2 = \frac{C_0}{4}$. Parallel gives $\frac{3C_0}{4} = \frac{3\varepsilon_0A}{4d}$ (B).

Final Answer:
$\frac{3A\varepsilon_0}{4d}$. \[ \boxed{\frac{3A\varepsilon_0}{4d}} \]