Conceptual Physics (12th Edition)

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

Chapter 23 - Think and Explain: 104

Answer

All are the same if 2 identical resistors are wired in parallel. The voltage across each is the same because they are resistors in parallel, no matter what. However, if the resistors are not identical, the one with greater resistance has less current through it, and less power dissipated in it.

Work Step by Step

For two or more devices connected in parallel, the voltage is the same across each device. This is Rule 1 for parallel circuits, on page 444, and discussed on pages 443-444. This is also illustrated in Figure 23.18. Ohm's Law states that the current through a resistor depends on the voltage, divided by the resistance. $$Current = \frac{voltage}{resistance}$$ For identical voltages, a larger resistance R means that the current is lower, as predicted by Ohm's Law. The power is P = (current)(voltage), so less power is dissipated in the larger R.
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