Final answer:
The energy stored in a 5.0 μF capacitor increases when the potential difference across its plates is raised from 0.40 V to 1.20 V, calculated using the formula U = 0.5 × C × V². The additional energy is found by subtracting the initial energy from the final energy.
Step-by-step explanation:
Understanding Capacitor Energy Storage
A capacitor is characterized by its ability to store electrical energy when a potential difference (voltage) is applied across its plates. The energy stored in a capacitor can be calculated using the equation U = 0.5 × C × V², where U is the energy in joules, C is the capacitance in farads, and V is the potential difference in volts.
Considering a 5.0 μF capacitor initially with a potential difference of 0.40 V, we apply the formula to find the initial energy stored, resulting in U_initial = 0.5 × (5.0 × 10⁻⁶ F) × (0.40 V)². When the potential difference is increased to 1.20 V, we calculate the new energy stored with U_final = 0.5 × (5.0 × 10⁻⁶ F) × (1.20 V)². The additional energy stored due to the increase in voltage is the difference between U_final and U_initial.
To find by what factor the stored energy is increased when the voltage is raised from 0.40 V to 1.20 V, we can take the ratio of the final energy to the initial energy. This demonstrates a clear relationship between the potential difference and the energy stored in a capacitor.