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: 52

Answer

The range is from $1\;M\Omega-15\;M\Omega$.

Work Step by Step

This is an estimation problem. Consider each of the times to be the time constant, RC, for the timer circuit. $$\tau=RC$$ Solve for the resistance. $$R=\frac{\tau}{C}$$ Now estimate the needed resistances for each of the given times. $$R_{1s}=\frac{\tau}{C}=\frac{1s}{1\times10^{-6}F}=1\times10^6\Omega$$ $$R_{2s}=\frac{\tau}{C}=\frac{2s}{1\times10^{-6}F}=2\times10^6\Omega$$ $$R_{4s}=\frac{\tau}{C}=\frac{4s}{1\times10^{-6}F}=4\times10^6\Omega$$ $$R_{8s}=\frac{\tau}{C}=\frac{8s}{1\times10^{-6}F}=8\times10^6\Omega$$ $$R_{15s}=\frac{\tau}{C}=\frac{15s}{1\times10^{-6}F}=15\times10^6\Omega$$ The range is from $1\;M\Omega-15\;M\Omega$.
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