The capacitance of a capacitor between` 4//3` times its original value if a dielectric slab of thickness `t=d//2` is inserted between the plates (d is the separation between the plates). What is the dielectric consant of the slab?

Options

A. 8
B. 4
C. 6
D. 2

Answer

To solve the problem step by step, we need to analyze the situation involving the capacitor and the dielectric slab.

### Step 1: Understand the Initial Capacitance
The initial capacitance \( C_0 \) of a parallel plate capacitor without any dielectric is given by the formula:
\[ C_0 = \frac{A \epsilon_0}{d} \]
where:
- \( A \) is the area of the plates,
- \( \epsilon_0 \) is the permittivity of free space,
- \( d \) is the separation between the plates.