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A capacitor holds a fixed amount of charge Q on its plates. If the top plate happens to carry the positive charge instead of the negative charge, how does this affect the sign of the electrical energy stored in the capacitor?
AThe stored energy stays positive either way
BThe stored energy becomes negative if the top plate is negative
CThe stored energy becomes zero if the charges are reversed
DThe stored energy doubles if the top plate is positive
Answer & Solution
Correct answer: A. The stored energy stays positive either way
1. Capacitor energy is given by U_E = (1/2) C V^2.
2. Squaring V removes any dependence on the sign of the voltage or which plate is positive.
3. Since C is always defined as positive and V^2 is never negative, U_E is always positive, no matter which plate carries which sign.
_Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.5 Capacitors and Dielectrics_
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