Electrical Engineering: Principles & Applications (6th Edition)

Published by Prentice Hall
ISBN 10: 0133116646
ISBN 13: 978-0-13311-664-9

Chapter 1 - 1.7 - Problems - Introduction to Circuits: P1.78

Answer

a) $I = I_1 + I_2 $ b) $I_1 = \frac{v}{15}; I_2 = \frac{v}{10}$ c) $v=24V$ d) Power is conserved.

Work Step by Step

a) Using Kirchhoff's Law, we find the current: $I = I_1 + I_2 $ b) Using the result from part a as well as Ohm's law, which states that $I=\frac{V}{R}$, we obtain: $I_1 = \frac{v}{15}; I_2 = \frac{v}{10}$ c) We use the fact that $I=4A$ to find: $ 4 = \frac{v}{15} + \frac{v}{10} \\ 4 = \frac{5v}{30} \\ 5v = 120 \\ \fbox{v=24V}$ d) We know that the power across a circuit is conserved, for energy is conserved. (If you want to verify this, you can use the equation for power to find the power of each circuit element: it will add up to $0W$.)
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