Final answer:
Electrostatic potential energy stored in a capacitor can be calculated using the formula Uc = ½ QV, accounting for the average voltage as the capacitor charges from zero to full voltage. This energy Uc is equivalent to the work done to charge the capacitor.
Step-by-step explanation:
The energy stored in a capacitor is known as electrostatic potential energy and can be calculated using the charge Q and the electric potential (voltage) V across the capacitor. The energy, Uc, is given by the equation:
Uc = ½ QV
This formula accounts for the fact that the capacitor starts from zero voltage and reaches the full voltage V as it charges. Since the first unit of charge experiences a voltage change (ΔV) of 0 and the final unit experiences ΔV = V, the average voltage across the capacitor is V/2.
Therefore, the total work W needed to charge the capacitor is equal to the energy Uc stored in it. For a capacitor with capacitance C, voltage V and charge Q, the energy in joules can also be calculated using the formula:
Uc = ½ CV^2 = ½ × (Q^2/C).