Each shot of the laser gun most favored by Rosa the Closer, the intrepid Vigilante of the lawless 22nd century, is powered by the discharge of a 1.41 F capacitor charged to 53.5 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor. She could do this by replacing the capacitor's lling, whose dielectric constant is 443, with one possessing a dielectric constant of 967. Find the electric potential energy U1 of the original capacitor when it is charged. An initially uncharged air-filled capacitor is connected to a 2.03 V charging source. As a result, the capacitor acquires 7.67 x 10- C of charge. Then, while the capacitor remains connected to the charging source, a sheet of dielectric material is inserted between its plates, completely filling the space. The dielectric constant k of this substance is 2.21. Find the voltage V across the capacitor and the charge Of stored by it after the dielectric is inserted and the circuit has returned to a steady state. V = V Of = CA paper-lled capacitor is charged to a potential difference of Vo = 2.3 V. The dielectric constant of paper is K = 3.7. The capacitor is then disconnected from the charging circuit and the paper lling is withdrawn, allowing air to ll the gap between the plates. Find the new potential difference V1 of the capacitor. While the capacitor is disconnected from the charging circuit, an unknown substance is inserted between the plates. The plates then attain a potential difference that is 0.67 times the original potential difference VO (when paper lled the capacitor). What is this unknown substance's dielectric constant K1]? K1]