Prove that in charging a capacitor half of the energy supplied by the battery is stored in the capacitor and remaining half is lost during charging.

Explanation

To prove that in charging a capacitor, half of the energy supplied by the battery is stored in the capacitor and the remaining half is lost during charging, we can follow these steps:

### Step 1: Determine the Energy Supplied by the Battery
When a capacitor of capacitance \( C \) is connected to a battery with voltage \( V \), the total charge \( Q \) on the capacitor is given by:
\[ Q = CV \]
The energy supplied by the battery (\( U_B \)) when charging the capacitor can be calculated as:
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