Question

Two parallel plate air capacitors are connected in parallel. Each capacitor has plate area \(A/2\) and separation between the plates is \(d\) and \(2d\) respectively. The equivalent capacity of the combination is

( \(ε_0\) = absolute permittivity of free space)

• A. \(\frac{Aε_0}{d}\)
• B. \(\frac{3Aε_0}{4d}\)
• C. \(\frac{2Aε_0}{3d}\)
• D. \(\frac{Aε_0}{4d}\)

Hint:

Add the two capacitances, each equal to epsilon0 times area over separation.

Answer 1

The Correct Option is B

Step 1: Each capacitor
Plate area is $A/2$ for both; gaps are $d$ and $2d$.

Step 2: Parallel sum
$C = \dfrac{\varepsilon_0A}{2}\left(\dfrac1d + \dfrac1{2d}\right) = \dfrac{\varepsilon_0A}{2}\cdot\dfrac{3}{2d}$.

Step 3: Result
$\dfrac{3\varepsilon_0A}{4d}$. Option (B).

Final Answer:
Option (B). \[ \boxed{\frac{3A\varepsilon_0}{4d}} \]