The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If $C$ is its initial capacitance, its final capacitance is equal to
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$C=\frac{\varepsilon_0 A}{d}$
Now, $C^{\prime}=\frac{\varepsilon_0( A / 2)}{2 d }=\frac{\varepsilon_0 A }{4 d }=\frac{ C }{4}$
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