Physics

Physics

Problem

2. A parallel-plate capacitor is charged by connection to a battery. If the battery is disconnected and the separation between the plates is increased, what will happen to the charge on the capacitor and the voltage across it? (A) Both remain fixed. (B) Both increase. (C) The charge increases and the voltage decreases. (D) The charge remains fixed and the voltage increases. (A) Both remain fixed. (B) Both increase. (C) The charge increases and the voltage decreases. (D) The charge remains fixed and the voltage increases.
Intuitive explanation

When you disconnect the battery, the charge QQ on the plates becomes trapped—there's nowhere for it to go. The key insight is that capacitance C=ϵ0A/dC = \epsilon_0 A / d depends on plate separation, so increasing dd decreases CC. Since V=Q/CV = Q/C and QQ is constant while CC shrinks, the voltage must increase. Think of it like squeezing the same amount of charge into a "weaker" capacitor.

Intuitive explanation

When you disconnect the battery, the charge QQ on the plates becomes trapped—there's nowhere for it to go. The key insight is that capacitance C=ϵ0A/dC = \epsilon_0 A / d depends on plate separation, so increasing dd decreases CC. Since V=Q/CV = Q/C and QQ is constant while CC shrinks, the voltage must increase. Think of it like squeezing the same amount of charge into a "weaker" capacitor.

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