Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 19 - DC Circuits - Problems - Page 554: 47

Answer

Add a 750 pF capacitor in parallel with the original 250 pF capacitor.

Work Step by Step

The energy stored by a capacitor can be expressed as $PE=\frac{1}{2}CV^2$. In order to store 4 times the energy, using the same battery and the same voltage V, the overall capacitance needs to increase by a factor of 4. A second capacitor, if it is connected in parallel to the first one, will have its capacitance add to that of the original. Therefore we should connect a capacitor in parallel whose capacitance is 3 times that of the original capacitor. This makes the final capacitance 4 times the original capacitance. We should add a 750 pF capacitor in parallel with the original 250 pF capacitor.
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