Two capacitors of unknown capacitance `C_(1) and C_(2)` are connected first in series and then in parallel, across a battery of 100V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively determine the values of `C_(1) and C_(2)`. Also calculate the charge on each capacitor in parallel combination.

Explanation

To solve the problem, we need to determine the values of the capacitances \( C_1 \) and \( C_2 \) based on the energy stored in the capacitors when connected in series and parallel. We will also calculate the charge on each capacitor in the parallel combination.

### Step 1: Understanding the Energy Formulas
The energy stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} C V^2 \]
Where:
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