An uncharged capacitor is connected to a battery. Show that half the energy supplied by the battery is lost as heat while charging the capacitor.

Explanation

To solve the problem of showing that half the energy supplied by the battery is lost as heat while charging the capacitor, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components**:
- Let the capacitance of the capacitor be \( C \).
- Let the voltage of the battery be \( V \).
- Initially, the capacitor is uncharged.
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