In vacuum, a parallel plate capacitor has capacitance `C_(0)`. New capacitance of sheet of thickness t and relative permittivity k is introduced between the plates is (take t=d):

Options

A. `C= (C_(0))/(k)`
B. `C= C_(0)`
C. `C=k C_(0)`
D. `C= (2)/(3) kC_(0)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Capacitance of a Parallel Plate Capacitor
The capacitance \( C_0 \) of a parallel plate capacitor in vacuum is given by the formula:
\[ C_0 = \frac{A}{d} \]
where \( A \) is the area of the plates and \( d \) is the separation between the plates.

### Step 2: Introduce the Dielectric Material
When a dielectric material with thickness \( t \) (in this case, \( t = d \)) and relative permittivity \( k \) is introduced between the plates, the capacitance changes. The new capacitance \( C \) with the dielectric is given by:
\[ C = \frac{k \cdot A}{d} \]

### Step 3: Relate the New Capacitance to the Original Capacitance
Since the original capacitance \( C_0 \) is \( \frac{A}{d} \), we can express the new capacitance \( C \) in terms of \( C_0 \):
\[ C = k \cdot \frac{A}{d} = k \cdot C_0 \]

### Step 4: Conclusion
Thus, the new capacitance \( C \) when the dielectric is introduced is:
\[ C = k \cdot C_0 \]

### Final Answer
The new capacitance of the capacitor with the dielectric sheet introduced is \( k \cdot C_0 \).

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