Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 25 - Capacitance - Questions - Page 739: 11

Answer

We can rank the arrangements according to the amount of charge stored: $C_1$ and $C_2$ in parallel $C_1$ $C_2$ $C_1$ and $C_2$ in series

Work Step by Step

Let $V$ be the battery voltage. We can write a general expression for the charge: $q = CV$ We can find an expression for the amount of charge stored in each situation: $C_1$ $q = C_1~V$ $C_2$ $q = C_2~V$ $C_1$ and $C_2$ in parallel: $q = (C_1+C_2)~V$ $C_1$ and $C_2$ in series: $q = (\frac{C_1~C_2}{C_1+C_2})~V$ Note that: $~~(C_1+C_2) \gt C_1 \gt C_2 \gt \frac{C_1~C_2}{C_1+C_2}$ We can rank the arrangements according to the amount of charge stored: $C_1$ and $C_2$ in parallel $C_1$ $C_2$ $C_1$ and $C_2$ in series
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