Final answer:
The exact capacitance required for each capacitor to store 1 J of energy in total cannot be determined without the voltage across the capacitors. When the voltage is known, the formula U = 1/2 C V^2 would be used to find the individual capacitance needed.
Step-by-step explanation:
To determine the capacitance required for each capacitor to store a total of 1 Joule (J) of energy when the capacitors are identical, we must consider the energy storage equation for a capacitor:
U = 1/2 C V^2
Here, U is the energy stored in Joules, C is the capacitance in Farads, and V is the potential difference across the capacitor in Volts. Since the capacitors are identical and we wish to store a total of 1 J of energy across both, we can rearrange the formula to solve for C when U is 0.5 J (as the energy will be split equally):
C = (2 U) / V^2
Without the voltage, we cannot solve for C directly from this question. However, if we were given the voltage across the capacitors, this formula could be used to find the capacitance required for each capacitor. Since the reference information provided mentions an equivalent capacitance of 4.0 µF for a different configuration, it is not directly applicable to this question.