Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 18 - Electric Currents - Problems - Page 522: 21

Answer

You would have to raise the temperature by $17.65^{\circ} C$ to $\approx 18^{\circ} C$.

Work Step by Step

The copper wire will remain essentially unchanged in length and cross-sectional area. Resistivity needs to increase by 12%. $ρ = ρ_{0} [1 + α (T - T_{0})]$ Plug 12% increase in. $ρ = ρ_{0} [1 + 0.12]$ $ \Delta T = T - T_{0}$ Set the portion inside the brackets equal to each other. $1 + α \Delta T = 1 + 0.12$ $\Delta T = \frac{0.12}{α}$ From the textbook for copper, $α = 0.0068 /^{\circ} C$ $\Delta T = \frac{0.12}{0.0068 /^{\circ} C}$ $\Delta T = 17.65 ^{\circ} C$ You would have to raise the temperature by $17.65^{\circ} C$.
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