A capacitor is conneted to a cell emf `E` having some internal resistance `r`. The potential difference across the

Options

A. cell is `lt E`
B. cell is E
C. capacitor is gtE
D. capacitor is `lt E`

Explanation

To solve the problem of finding the potential difference across a capacitor connected to a cell with internal resistance, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit Configuration**:
- We have a capacitor with capacitance \( C \) connected to a cell with an electromotive force (emf) \( E \) and an internal resistance \( r \).
- The circuit can be visualized as a capacitor in series with the internal resistance of the cell.

2. **Identify the Steady State Condition**:
- When the capacitor is fully charged, it reaches a steady state. In this condition, the current flowing through the circuit becomes zero.
- This is because a fully charged capacitor acts like an open circuit, meaning no current can flow through it.

3. **Apply Kirchhoff’s Voltage Law**:
- According to Kirchhoff’s Voltage Law, the sum of the potential differences in a closed loop must equal zero.
- In our case, the potential difference across the cell (emf \( E \)) must equal the potential difference across the capacitor plus the potential drop across the internal resistance \( r \).

4. **Current in Steady State**:
- Since the current \( I \) in the circuit is zero when the capacitor is fully charged, we can express this as:
\[ I = 0 \]
- Therefore, the voltage drop across the internal resistance \( r \) is:
\[ V_r = I \cdot r = 0 \cdot r = 0 \]

5. **Determine the Potential Difference Across the Capacitor**:
- Since the current is zero, the entire emf \( E \) is applied across the capacitor. Thus, the potential difference across the capacitor \( V_C \) is:
\[ V_C = E - V_r = E - 0 = E \]

6. **Conclusion**:
- The potential difference across the capacitor, when it is fully charged, is equal to the emf of the cell, which is \( E \).

### Final Answer:
The potential difference across the cell is \( E \).