When a charged capacitor is connected with an uncharged capacitor , then which of the following is /are correct option/options.

Options

A. the magnitude of charge on the charged capacitor decreases.
B. a steady state is obtained after which no further flow of charge occurs.
C. the total potential energy stored in the capacitors remains conserved.
D. the charge conservation is always true.

Answer

To solve the question regarding the behavior of a charged capacitor when connected to an uncharged capacitor, let's break down the process step by step.

### Step-by-Step Solution:

1. **Understanding Capacitors**:
- A capacitor stores electrical energy in the form of an electric field. When charged, it has a certain amount of charge (Q) and a potential difference (V) across its plates.

2. **Connecting Capacitors**:
- When a charged capacitor (let's call it Capacitor 1) is connected to an uncharged capacitor (Capacitor 2), charge will flow from Capacitor 1 to Capacitor 2 until the potential difference across both capacitors is equal.

3. **Charge Flow**:
- The charged capacitor (Capacitor 1) has a potential difference across its plates. When connected to the uncharged capacitor (Capacitor 2), charge will flow from the positively charged plate of Capacitor 1 to the uncharged plate of Capacitor 2 until the voltage across both capacitors equalizes.

4. **Change in Charge**:
- As charge flows from Capacitor 1 to Capacitor 2, the magnitude of charge on Capacitor 1 decreases. This is because some of its charge is now stored in Capacitor 2.

5. **Steady State**:
- A steady state is reached when the potential difference across both capacitors is the same. At this point, no further flow of charge occurs.

6. **Total Energy Consideration**:
- The total potential energy stored in the system remains conserved. While energy may redistribute between the two capacitors, the total energy before and after the connection remains the same, assuming ideal conditions (no losses).

7. **Conservation of Charge**:
- The principle of conservation of charge states that the total charge in an isolated system remains constant. Therefore, the total charge before and after the connection remains the same.

### Conclusion:
Based on the above analysis, we can conclude that:
- The magnitude of charge on the charged capacitor decreases (Correct).
- A steady state is obtained after which no further flow of charge occurs (Correct).
- The total potential energy stored in the capacitors remains conserved (Correct).
- The conservation of charge is always true (Correct).

Thus, all options (A, B, C, D) are correct.