Find an expression for the capacitance of a parallel plate capacitor when a dielectric slab of dielectric constant K and thickness `t=(d)/(2)` but the same area on the plates is inserted between the the capacitors plate. (d=separation between the plates)

Explanation

To find the expression for the capacitance of a parallel plate capacitor when a dielectric slab of dielectric constant \( K \) and thickness \( t = \frac{d}{2} \) is inserted between the plates, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have a parallel plate capacitor with plate separation \( d \).
- A dielectric slab of thickness \( t = \frac{d}{2} \) is inserted between the plates.
- The remaining distance between the plates, without the dielectric, is \( \frac{d}{2} \).
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