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## Homework Statement

The currents ##I_{{a}}## and ##I_{{b}}## of the circuit have values 4A and -2A in that respective order.

A) Find ##I_{{g}}##

B) Find the power dissipated by each resistance

C) Find ##V_{{g}}## (voltage drop across the current source)

D) Show that the power delivered by the current source is equal to that dissipated by every other circuit element.

See attachment "primero" for the circuit image.

## Homework Equations

Kirchoff’s DC circuits laws only, no resistive simplification neither nodal analysis.

## The Attempt at a Solution

By assuming that the negative current means that the current is flowing in the other direction, and some time trying to try me best to figure out how current circulated across all the circuit, I got attachment "segundo".

Now to my attempt, first, I wrote 4 KCEQ and 2 KVEQ: $$N_{{1}}:4A+2A=I_{{c}}, I_{{c}}=6A$$ $$N_{{2}}:I_{{d}}+I_{{c}}=I_{{g}}$$ $$N_{{3}}:I_{{d}}+2A=I_{{e}}$$ $$N_{{4}}:I_{{g}}=I_{{e}}+4A$$ $$V_{{4214}}:-V_{{g}}+30V+100V+60V=0, V_{{g}}=190V$$ $$V_{{4234}}:-190V+I_{{d}}*30\,\Omega+I_{{e}}*4\,\Omega+I_{{e}}*16\,\Omega=0$$

As you can see, ##V_{{g}}## and ##I_{{c}}## were easy to obtain. Then using ##N_{{3}}## I sustituted it in ##V_{{4234}}## to obtain that ##I_{{d}}=3A##, then plugged in ##N_{{2}}## to get the value of ##I_{{g}}##, 9A.

Until now, A and C are done, then by doing ##P=I^2*R## in each resistance I got 1310W for answer B.

For D, I calculated the current source power generated, which was ##-I*V## that got me 1710W, which is the answer from B plus the power consumed by the voltage source, then all the exercises are correct, BUT: My real question, and problem, is if I correctly indicated all the current circulations in the second attachment, because I want to know if it really matters after all to get the correct answer!

Thanks.