consider a charged parallel-plate capacitor. how can its capacitance be halved?,

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The capacitance of a charged parallel-plate capacitor can be halved by doubling the area of its plates and keeping their separation constant. This is achieved by placing another identical, uncharged, parallel plate in between the original two. We have seen that when we increase the area of a charged capacitor’s plates while keeping them separated at intervals identical to those in our original configuration, then we reduce the total capacitance of our system. Now let us consider what happens if we do this but instead place an additional uncharged plate with dimensions one half as large as those of the original two separating them? Since each plate is now the same size as our original plates, but their separation has been doubled (i.e., we’ve added a new plate), then the total capacitance of our system will be one-half that of what it was in its initial configuration. This fact may seem puzzling to those who are unfamiliar with this effect, which can be understood by considering how much energy would need to flow into or out of our capacitor if equilibrium were not maintained for reasons outside the scope of this post. In conclusion: If you want your charged parallel-plate capacitor to have half the capacitance when charged and uncharged than before, simply double both its area and keep them separated at intervals identical to those in your


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