Question
In a very simple circuit consisting of a battery and a capacitor with an adjustable distance between the plates, how does the voltage vary as the distance is altered?
Final Answer
The voltage doesn't vary with changes in distance between the plates. Voltage is controlled by the battery. The amount of charge on each plate of the capacitor is what changes with changes in separation.
Solution video
OpenStax College Physics for AP® Courses, Chapter 19, Problem 32 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. We are told that there's a circuit with a battery and a capacitor in series and the plates of this capacitor have an adjustable distance between them so this d can be increased or decreased and what will happen to the voltage between the plates of the capacitor as the distance is changed? And the answer is there will be no change in the voltage of the capacitor because the voltage is determined by the battery. So the battery has some emf or some voltage and the capacitor will therefore have the same emf but you must be thinking... well, something's gotta change and the answer to that is yes... but it's the amount of charge on each plate that will change because the capacitance for a parallel plate capacitor is this permittivity of free space times the area of the plate divided by the distance between them and we can also say capacitance is the amount of charge stored in each plate divided by the voltage between the plates in which case Q equals C times V and then we can substitute for C and see that Q varies with d inversely so Q is inversely proportional to d in which case as d increases, the amount of charge stored on each plate will decrease but this says nothing about the voltage, the voltage again is just determined by the battery that the capacitor is connected to.