1.)If you want to double the energy stored in a given capacitor, by what factor

Question

1.)If you want to double the energy stored in a given capacitor, by what factor should you change the charge on its plates?

2.)When a parallel-plate capacitor is connected across a certain battery, the energy stored in its plates is U_0 . If you keep it connected, but move its plates so that the distance between them is now half of what it was, what is the energy it stores, in terms of U_0 ?

3.)If connecting a capacitor across a 30.0 { m V} battery stores 11.0 { m J} of energy in the capacitor, how much energy will be stored if you increase the battery setting by 50.0 { m V}?

Explanation / Answer

1. sqrt(2) because U is directly proportional to q^2
2. 2 U_0, distance and energy stored are inversely proportional.
3. (80/30)2 x 11

I used the equation U= (1/2C)q2 to get these answers.

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