University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 24 - Capacitance and Dielectrics - Problems - Exercises - Page 813: 24.60

Answer

In parallel $Q = 7.2 \times 10^{-3}\,\text{C}$ and in series $Q = 0.654 \times 10^{-3}\,\text{C} $

Work Step by Step

We have two circuits, first when the capacitors are in parallel where, in parallel, the equivalent capacitance is given by $$C_{eq} = 10 \mathrm{~\mu F} + 20 \mathrm{~\mu F} +30 \mathrm{~\mu F} = 60 \mathrm{~\mu F} $$ We could get the charge and it is calculated by $$Q = C_{eq} V = (60 \times 10^{-6}\,\text{F}) (120 \,\text{V}) = \boxed{7.2 \times 10^{-3}\,\text{C}} $$ Second, when the capacitors are in series where, in series, the equivalent capacitance is given by $$\dfrac{1}{C_{eq} }= \dfrac{1}{10 \mathrm{~\mu F} } + \dfrac{1}{20 \mathrm{~\mu F}} + \dfrac{1}{30 \mathrm{~\mu F} } $$ $$C_{eq} = 5.45\mathrm{~\mu F}$$ We could get the charge and it is calculated by $$Q = C_{eq} V = (5.45 \times 10^{-6}\,\text{F}) (120 \,\text{V}) = \boxed{0.654 \times 10^{-3}\,\text{C}} $$
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