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 810: 24.21

Answer

(a) ${C_{eq}}' = 19.3 \mathrm{~n F} $ (b) $ Q = 482.5 \mathrm{~n C}$ (c) $Q = 162.5 \mathrm{~n C}$ (d) $V = 25 \,\text{V}$

Work Step by Step

a) For the capacitor in series, they have an equivalent capacitance calculated by $$\dfrac{1}{C_{eq}} = \dfrac{1}{18\mathrm{~ nF} } + \dfrac{1}{30 \mathrm{~nF} } +\dfrac{1}{10 \mathrm{~nF} } = 0.188 $$ Take the reciprocal $$C_{eq} = 5.30 \mathrm{~n F} $$ For the capacitor in parallel, they have an equivalent capacitance calculated by $${C_{eq}}' = C_{eq} + 7.5 \mathrm{~nF} + 6.5 \mathrm{~n F} = \boxed{19.3 \mathrm{~n F} }$$ (b) The charges of the system are given by $$Q = {C_{eq}}' V_{ab}$$ Where $V_{ab}$ is the potential between the two terminals. Let us substitute the values $C$ and $V_{ab}$ to get the charge on each plate $$Q = {C_{eq}}' V_{ab} = (19.3 \mathrm{~n F})(25 \,\text{V}) = \boxed{482.5 \mathrm{~n C}}$$ (c) $$Q = CV= (6.5 \mathrm{~n F})(25 \,\text{V}) = \boxed{162.5 \mathrm{~n C}}$$ (d) 7.5 nF has the same potential of the system as it in parallel with the remaining elements $$\boxed{V = 25 \,\text{V}}$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.