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: Capacitance of each:
Each plate area is \(\frac A2\). \(C_1 = \frac{\varepsilon_0(A/2)}{d} = \frac{\varepsilon_0A}{2d}\) and \(C_2 = \frac{\varepsilon_0(A/2)}{2d} = \frac{\varepsilon_0A}{4d}\).

Step 2: Parallel combination:
\[ C = C_1 + C_2 = \frac{\varepsilon_0A}{2d} + \frac{\varepsilon_0A}{4d} = \frac{3\varepsilon_0A}{4d} \]
Using series by mistake would give \(\frac{\varepsilon_0A}{6d}\), which is not an option, so the parallel rule is the right one.

Final Answer:
The equivalent capacity is \(\frac{3A\varepsilon_0}{4d}\), option (B). \[ \boxed{\frac{3A\varepsilon_0}{4d}} \]