Assertion: Two capacitors are connected in series with a battery. Energy stored across them is in inverse ratio of their capacity.
Reason: `U=1/2qV` or `UpropqV`

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "Two capacitors are connected in series with a battery. Energy stored across them is in inverse ratio of their capacity."

When capacitors are connected in series, they share the same charge (Q). The energy stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} Q V \]
where \( V \) is the voltage across the capacitor.

### Step 2: Energy Stored in Each Capacitor
For two capacitors \( C_1 \) and \( C_2 \) connected in series, the total voltage \( V \) is divided between the two capacitors. The voltage across each capacitor can be expressed as:
\[ V_1 = \frac{Q}{C_1} \]
\[ V_2 = \frac{Q}{C_2} \]

The energy stored in each capacitor can be calculated as follows:
- For capacitor \( C_1 \):
\[ U_1 = \frac{1}{2} Q V_1 = \frac{1}{2} Q \left(\frac{Q}{C_1}\right) = \frac{Q^2}{2C_1} \]

- For capacitor \( C_2 \):
\[ U_2 = \frac{1}{2} Q V_2 = \frac{1}{2} Q \left(\frac{Q}{C_2}\right) = \frac{Q^2}{2C_2} \]

### Step 3: Ratio of Energies
Now, we can find the ratio of the energies stored in the two capacitors:
\[ \frac{U_1}{U_2} = \frac{\frac{Q^2}{2C_1}}{\frac{Q^2}{2C_2}} = \frac{C_2}{C_1} \]

This shows that the energy stored in the capacitors is indeed in the inverse ratio of their capacitances, confirming the assertion.

### Step 4: Analyze the Reason
The reason states: "U = 1/2 qV or U is proportional to qV."

This is a true statement as the energy stored in a capacitor is given by \( U = \frac{1}{2} Q V \). However, while this statement is true, it does not directly explain why the energy stored in the capacitors is in inverse ratio to their capacitance when connected in series.

### Conclusion
Both the assertion and the reason are true, but the reason does not correctly explain the assertion. Therefore, the correct answer to the question is:
**B: Both assertion and reason are true, but the reason is not a correct explanation for the assertion.**

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