Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set: 49

Answer

$R_{eq}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$

Work Step by Step

The equivalent resistance of two resistors connected in parallel is given by the following the expression: $R_{eq}=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}$ Evaluate the sum indicated in the denominator: $\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}=\dfrac{1}{\dfrac{R_{2}+R_{1}}{R_{1}R_{2}}}=...$ Evaluate the division and simplify: $...=1\div\dfrac{R_{1}+R_{2}}{R_{1}R_{2}}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$ This simplified expression represents the equivalent resistance of two resistors in parallel: $R_{eq}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$
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