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Answer :
Using the formula for the energy stored in a capacitor and the given values, it's calculated that approximately 8.36 capacitors are needed to store 95.7J of energy, so 9 capacitors are required as we round up to the nearest whole number.
To calculate the number of capacitors needed to store a specific amount of energy, we use the formula for the energy stored in a capacitor,[tex]U = rac{1}{2}CV^2[/tex], where U is the energy in joules, C is the capacitance in farads, and V is the potential difference in volts. For capacitors in parallel, the total capacitance [tex]C_{total}[/tex] is equal to the sum of their individual capacitances: [tex]C_{total} = nC[/tex], where n is the number of capacitors.
The energy stored in a capacitor can be calculated using the formula E = 0.5 * C * V^2, where E is the energy, C is the capacitance, and V is the potential difference. By calculating the energy stored by each capacitor and finding the total energy stored by all capacitors in parallel, we can determine the number of capacitors required to store 95.7% of the total energy.
By dividing the total energy stored by the energy needed (95.7% of the total energy), we can find the number of capacitors required to reach the desired energy storage level.
Since we can't have a fraction of a capacitor, we need 9 capacitors to store at least 95.7J of energy.
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