Answer :
The 12 V and 1.0 F combination will store the most energy in a capacitor, according to the formula E = 1/2 C V^2, because it has the highest voltage and capacitance. Therefore the correct option is 12 V & 1.0 F.
The combination of a battery and capacitor that will store the most energy in the capacitor can be found by using the formula for the energy stored in a capacitor, which is given by E = 1/2 C V^2, where E is the energy in joules, C is the capacitance in farads, and V is the potential difference in volts.
To maximize the energy stored, we need to maximize both the capacitance (C) and the square of the voltage (V^2). Thus, without calculation, we can see that the 12 V & 1.0 F combination will store the most energy because it has the highest voltage and the highest capacitance.
For example, applying the formula to this combination: E = 1/2 * 1.0 F * (12 V)^2 = 1/2 * 1.0 * 144 = 72 J. This is clearly higher than any other combination with either a lower voltage (6 V) or lower capacitance (0.1 F).
