PHYSICS: Capacitor Concept Question There are two very similar questions with op

Question

PHYSICS: Capacitor Concept Question

There are two very similar questions with opposite answers, and I do not understand why:

Scenario #1:

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will ____DOUBLE_____

Scenario #2

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference between the plates. If the separation between the plates is doubled, the magnitude of the electrical energy stored on the capacitor will ____ BE CUT IN HALF_____

These are the CORRECT answers to both questions, but I do not understand why. Please explain how these questions are different, as well as any formulas involved in the reasoning process.

Explanation / Answer

(a)

C=A/d

C is in inverse propotional to d

U =(1/2)* Q^2/C This equation is used since Q stays constant.

So that U is in propotion to d.

if d doubles..U doubles.

(b) when voltage from bettary stays constant

U = (1/2)*C* V^2 here, V=C

U is in onverse proportion to d

d doubles..U halves.

Difference is in first case Q stays constant and in second case V stays constant.

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