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

Question

A parallel-plate capacitor with air between the plates is connected to a battery. The following steps are then carried out, but you get to decide in what order they are done. Step A - disconnect the battery. Step B - reduce the distance between the plates by a factor of 2. Step C - increase the distance between the plates by a factor of 3. (a) If your goal is to maximize the potential difference across the capacitor, in what order should you carry out the steps? First do A, then B, then C. First do B, then A, then C. Do steps A and B in either order, and then do step C. First do A, then C, then B. First do C, then A, then B. Do steps A and C in either order, and then do step B. First do B, then C, then A. First do C, then B, then A. Do steps B and C in either order, and then do step A. Let?s say you now compare the following two procedures, starting from the same initial configuration with the capacitor connected to the battery. Procedure 1: First do step B, then C, then A. Procedure 2: First do step C, then A, then B. (b) The ratio of the potential difference across the capacitor after procedure 1 to the potential difference across the capacitor after procedure 2 is

Explanation / Answer

a) if you do B then A then C

since still connected, B wont do anything

then after disconnecting, icnreasing the distance will make V triple

so First do B, then A, then C

b)

if you do B, then C, then A, V wont change since always on battery while other things changed so V = Vinitial

if C then A then B, C wont matter since still connected, B will halve the V

so V1/V2 = V0/(0.5 v0) = 2

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