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: P1.79

Answer

a) $v_1 + v_2 = v$ b) $v_1 = 3I; v_2 = 4I $ c) $v = 14V$ d) Power is conserved.

Work Step by Step

a) We use Kirchhoff's Voltage Law, which states that the voltage around any closed loop in a circuit is 0, to find: $-v + v_1 + v_2 = 0 \\ v = v_1 + v_2$ b) We know from Ohm's law that $V=IR$. Thus, plugging in the values for resistance, we find: $v_1 = 3I; v_2 = 4I $ c) We know that there is a current of 2A, so we use the results from parts a and b to find: $v = 3I + 4I \\ v = 7I \\ V = 7(2) = \fbox{14V}$ 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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