A parallel-plate capacitor has plates of area (A). The plates are initially separated by a distance (d),

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A parallel-plate capacitor has plates of area \(A\). The plates are initially separated by a distance \(d\), but this distance can be varied. If the capacitor is connected to a battery, what should the plate separation be if you want to quadruple \((a)\) the capacitance, \((b)\) the charge stored, (c) the energy stored, and (d) the energy density?

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