A capacitor of capacitance `C` which is initially charged up to a potential differnce `epsilon` is connected with a battery of emf `epsilon/2` such that the positive terminal of the battery is connected with the positive plate of the capacitor. Find the heat loss in the circuit the process of charging.

Explanation

To solve the problem step by step, we will analyze the situation involving the capacitor and the battery, calculate the initial and final energy stored in the capacitor, and then find the heat loss during the charging process.

### Step 1: Calculate the initial energy stored in the capacitor
The initial energy \( U_i \) stored in a capacitor is given by the formula:
\[ U_i = \frac{1}{2} C E^2 \]
where \( C \) is the capacitance and \( E \) is the initial potential difference.
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