Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 44: 97

Answer

$a)$ $R=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$ $b)$ $R=\dfrac{20}{3}$ $\Omega\approx6.67$ $\Omega$

Work Step by Step

$R=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}$ $a)$ Evaluate the sum of fractions in the denominator: $R=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}=\dfrac{1}{\dfrac{R_{1}+R_{2}}{R_{1}R_{2}}}=...$ Evaluate the division: $...=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$ $b)$ $R_{1}=10$ $\Omega$ and $R_{2}=20$ $\Omega$ Substitute the values of $R_{1}$ and $R_{2}$ into the solution found on part $a)$ and evaluate to find the total resistance: $R=\dfrac{(10)(20)}{10+20}=\dfrac{200}{30}=\dfrac{20}{3}$ $\Omega\approx6.67$ $\Omega$
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