A parallel-plate capacitor with air between the plates is connected to a 12-volt

Question

A parallel-plate capacitor with air between the plates is connected to a 12-volt battery. What is the potential difference across the capacitor? Without bringing in additional batteries, is it possible to increase the potential difference across the capacitor to 36 V, by making changes such as removing the battery and/or changing the separation between the plates? If so, how can it be done? Yes, it is possible. With the battery still connected to the capacitor, decrease the spacing between the plates by a factor of 3. Yes, it is possible. With the battery still connected to the capacitor, increase the spacing between the plates by a factor of 3. Yes, it is possible. With the battery still connected to the capacitor, decrease the spacing between the plates by a factor of 3, and then disconnect the battery. Yes, it is possible. With the battery still connected to the capacitor, increase the spacing between the plates by a factor of 3, and then disconnect the battery. Yes, it is possible. First, disconnect the battery, and then decrease the spacing between the plates by a factor of 3. Yes, it is possible. First, disconnect the battery, and then increase the spacing between the plates by a factor of 3. Yes, it is possible, but none of the methods outlined above will work. No, it is not possible to start with 12 V and end up with 36 V.

Explanation / Answer

1) 12 volts

2) so if you connect it and bring the battery to 12,

then disconnect,

Q = C V,

Q will remain constant so if your make C go down by a third V will triple

so C = e0 A/d

so you need to triple the spacing

so yes it is possible, disconnect the battery and increase the spacing by a a factor of 3

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