Conceptual Physics (12th Edition)

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

Chapter 23 - Think and Discuss: 120

Answer

a. The equivalent resistance is $4 \Omega$. b. 6 A. c. 2 A.

Work Step by Step

a. A pair of resistors wired in series has an equivalent resistance equal to the sum of the resistances. This is Rule 2 on page 443. The top branch then has an equivalent resistance of $12 \Omega$ and so does the bottom branch. We now effectively have three $12 \Omega$ resistors in parallel. The equation is not given in this textbook, but for 3 resistors in parallel, the following relation holds. $$\frac{1}{R_{parallel}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} $$ Apply the equation to this problem. $$\frac{1}{R_{parallel}} = 3 \times \frac{1}{12 \Omega} = \frac{1}{4 \Omega} $$ $$R_{parallel} = 4 \Omega$$ b. $I = \frac{V}{R} = \frac{24V}{4 \Omega} = 6 A$. c. $I = \frac{V}{R} = \frac{24V}{12 \Omega} = 2 A$.
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