Passage II
We have two parallel plate capacitors P and Q having same capacitance `C_(0)`. P is connected to a battery of potential difference V and it remains connected to the battery even after the charging is over. Q is also connected to a battery of the same potential difference V but after the charging gets over, it is disconnected from the battery.
Answer the following questions:
Potential difference between the plates of P, when a dielectric slab is inserted in between the plates

Options

A. increases
B. decreases
C. remains same
D. first increases and after some time becomes same as before

Explanation

To find the potential difference between the plates of capacitor P when a dielectric slab is inserted, we will follow these steps:

### Step 1: Understand the Initial Conditions
Capacitor P has a capacitance \( C_0 \) and is connected to a battery with a potential difference \( V \). When fully charged, the charge \( Q \) on capacitor P can be expressed as:
\[ Q = C_0 \cdot V \]

### Step 2: Insert the Dielectric Slab
When a dielectric slab with dielectric constant \( k \) is inserted between the plates of capacitor P, the capacitance of the capacitor changes. The new capacitance \( C' \) becomes:
\[ C' = k \cdot C_0 \]

### Step 3: Analyze the Connection to the Battery
Since capacitor P remains connected to the battery even after charging, the potential difference across it will still be maintained at \( V \). The battery will adjust the charge on the capacitor to keep the potential difference constant.

### Step 4: Calculate the New Charge
With the new capacitance \( C' \), the charge \( Q' \) on capacitor P can be expressed as:
\[ Q' = C' \cdot V = (k \cdot C_0) \cdot V \]

### Step 5: Determine the Potential Difference
Since the capacitor P remains connected to the battery, the potential difference across the plates of capacitor P does not change when the dielectric slab is inserted. Therefore, the potential difference remains:
\[ V' = V \]

### Conclusion
The potential difference between the plates of capacitor P when a dielectric slab is inserted remains the same as the original potential difference \( V \).

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