Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 6 - Section 6.7 - Formulas - Exercises - Page 256: 21

Answer

$$f=\frac{1}{2X_C \pi C} .$$

Work Step by Step

To solve the equation for $f$, we multiply both sides by $2\pi f C$ and then divide both sides by $2\pi CX_C$ as follows: $$X_C=\frac{1}{2\pi fC} \Longrightarrow2X_C f\pi C=1\Longrightarrow \frac{2X_C f\pi C}{2X_C \pi C}=\frac{1}{2X_C \pi C}\\ \Longrightarrow f=\frac{1}{2X_C \pi C} .$$
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