A parallel-plate capacitor consists of two conducting plates with a surface area of \(1.0 \mathrm{~m}^{2}\) and a plate separation distance of \(50 \mu \mathrm{m}\).

(a) Determine the capacitance and the energy stored in the capacitor when it is charged by connecting it to a \(9.0-\mathrm{V}\) battery.

(b) With the capacitor fully charged and disconnected from the battery, a \(50-\mu \mathrm{m}\)-thick sheet of Mylar is inserted between the plates. Determine the potential difference across the capacitor and the energy stored in it.

(c) If the Mylar-filled capacitor is connected to the battery, how much work does the battery do to fully charge the capacitor?