Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 23 - Think and Solve: 51

Answer

The current decreases to 90 percent of its original value, to 9 A. The power decreases to 81 percent of its original value, to 972 W.

Work Step by Step

Find the resistance of the coffeemaker. $$Current = \frac{voltage}{resistance}$$ Rearranging to solve for the resistance, we obtain $$Resistance= \frac{voltage}{current}$$ Put the numbers in from this problem. $$Resistance= \frac{120 V}{10 A} = 12 \Omega$$ What current will flow when the voltage is cut to 90 percent of 120 V, or 108 V? $$Current = \frac{voltage}{resistance}$$ $$I = \frac{108 V}{12 \Omega} = 9 A$$ $$Electric \; power = (current) \times (voltage)$$ $$P = (9 A)(108 V) = 972 W$$ Summary: Current and voltage both decreased by 10 percent. The power, which is their product, decreased by 19 percent (because (0.9)(0.9) = 0.81 = 1 - 0.19).
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