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## Homework Statement

Find the power being absorbed by element X in Figure if it is a (a) 100 Ω resistor; (b) 40 V independent voltage source, + reference on top; (c) dependent voltage source labeled 25ix ,+ reference on top; (d) dependent voltage source labeled 0.8v1,+ reference on top; (e) 2 A independent current source, arrow directed upward.

## Homework Equations

[tex]P = vi[/tex]

## The Attempt at a Solution

a)

KVL:

[tex]20v + R_{1}i - 120v + R_{2}i + R_{3}i + R_{4}i + R_{5}i[/tex]

[tex]i = \frac{20v - 120v}{R_{1} + R_{2} + R_{3} + R_{4} + R_{5}}[/tex]

[tex]i = \frac{-100v}{200\Omega} = -0.5A[/tex]

[tex]v = Ri = (100\Omega)(-0.5A) = -50v[/tex]

[tex]P = (-50v)(-0.5A) = 25w[/tex]

b)

KVL:

[tex]20v + R_{1}i - 120v + R_{2}i + R_{3}i + R_{4}i + 40v[/tex]

[tex]i = \frac{20v + 40v - 120v}{R_{1} + R_{2} + R_{3} + R_{4}}[/tex]

[tex]i = \frac{-60v}{100\Omega} = -0.6A[/tex]

[tex]P = (40v)(-0.6A) = -24w[/tex]

c)

KVL:

[tex]20v + R_{1}i - 120v + R_{2}i + R_{3}i + R_{4}i[/tex]

[tex]i = \frac{20v - 120v}{R_{1} + R_{2} + R_{3} + R_{4}}[/tex]

[tex]i = \frac{-100v}{100\Omega} = -1A[/tex]

[tex]P = ((25)(-1A))(-1A) = 25w[/tex]

d)

current is same as c)

[tex]i = -1A[/tex]

[tex]v_{1} = (40\Omega)(-1A) = -40v[/tex]

[tex]P = ((0.8)(-40v))(-1A) = 32w[/tex]

e)

I am not sure how to do e) because I don't have a voltage and the current is 2A.