Circuit Analysis: Find i, v Given R1, R2

[Xkaliber]

Homework Statement

(a) Suppose that R_1 = 6 ohms and R_2 = 3 ohms. Find the current i and the voltage v. See the diagram in the picture.

http://img291.imageshack.us/img291/7638/picturewr3.th.jpg

Homework Equations

Kirchhoff's laws and Ohm's law

The Attempt at a Solution

I got v=12V and i=1A

However, I do not think that this is correct since a positive value for i means the voltage source is absorbing energy instead of supplying it, which does not make sense.

 

[LowlyPion]

I got v=12V and i=1A

However, I do not think that this is correct since a positive value for i means the voltage source is absorbing energy instead of supplying it, which does not make sense.

Why don't you write out your current loop equations and maybe we can see where you may be confused?

 

[Xkaliber]

First, since the 3 amp current source is in series with R_2, the current through R_2 is 3A. Using Ohm's law, we find the voltage across R_2 to be 9 volts.

Now, KVL around outer loop: -12V - 9V + v = 0 -> v = 21V

KVL around right smaller loop: -9V + 21V - v_1 = 0 -> v_1 = 12V

Using ohm's law, current through R_1 = 2A

KCL @ top middle node: 3A - 2A - i = 0 -> i = 1A

If i does equal 1A, then according to the diagram in the picture, the voltage source is absorbing power since it is in the passive convention.

 

[LowlyPion]

Now, KVL around outer loop:

This could be your problem.

I think what you really want to do is take the equations for the left and right loops, noting that the current through the R₁ is the sum of the left and right loop currents.

This should give ou the equations and unknowns that you are looking for.