Final answer:
To calculate the energy stored in a capacitor network, one can use the formula U = ½ CV².
Series and parallel arrangements affect total capacitance and energy storage, with series connections dividing the potential difference and parallel connections having the same potential difference across each capacitor.
Step-by-step explanation:
To find the total energy stored in a capacitor network, the formula U = ½ CV² is used, where U is the energy, C is the capacitance, and V is the potential difference.
For three capacitors in series with capacitances of 8.4 μF, 8.4 μF, and 4.2 μF, the equivalent capacitance (Ceq) can be calculated by using the reciprocal formula for series capacitors: 1/Ceq = 1/8.4 + 1/8.4 + 1/4.2. After finding the equivalent capacitance, the total energy stored in the series network can be calculated. When capacitors are connected in parallel, their capacitances simply add up.
Therefore, the total capacitance is the sum of all three, and the energy can be recalculated using the same energy formula but with the new total capacitance and the initial potential difference.
Regarding the potential difference across each capacitor in a series arrangement, it will vary since capacitors in series divide the potential difference. However, in a parallel arrangement, all capacitors experience the same potential difference as the original source.
The equation to determine the energy stored in an individual capacitor is U = ½ CV², where C is the individual capacitance of a capacitor and V is the potential difference across that specific capacitor.
The energy stored in the capacitor network is influenced by capacitor arrangement. In a series connection, the voltage divides among the capacitors while in parallel, each capacitor is charged up to the voltage of the source. This results in different energies stored for series and parallel configurations.