Final answer:
The factor by which the potential energy stored in the capacitor changes is 0.22.
Step-by-step explanation:
The potential energy stored in a capacitor is given by the equation U = 1/2 * C * V^2, where U is the energy, C is the capacitance, and V is the voltage across the capacitor. In this case, the potential difference across the capacitor is increased from 0.40 V to 1.20 V. To find the factor by which the energy is increased, we can use the formula:
Factor = (Uf - Ui) / Ui = (1/2 * C * Vf^2 - 1/2 * C * Vi^2) / (1/2 * C * Vi^2), where Uf and Ui are the final and initial energies, Vf and Vi are the final and initial voltages.
Plugging in the given values, we have:
Factor = (1/2 * 5.0 * 10^(-12) * (1.20)^2 - 1/2 * 5.0 * 10^(-12) * (0.40)^2) / (1/2 * 5.0 * 10^(-12) * (0.40)^2) = 0.22.
Therefore, the factor by which the energy stored in the capacitor is increased is 0.22, option b.