High School

You have two different batteries, 6 V and 12 V, and two different capacitors, 0.1 F and 1.0 F. Which combination of battery and capacitor will store the most energy in the capacitor?

A. 6 V battery (either capacitor)
B. 6 V & 1.0 F
C. 12 V battery (either capacitor)
D. 12 V & 0.1 F
E. 6 V & 0.1 F
F. 1.0 F capacitor (either battery)
G. 12 V & 1.0 F
H. 0.1 F capacitor (either battery)

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).