How Do You Calculate Voltage and Power in a 12-Ohm Resistor Circuit?

[calcuseless]

Homework Statement

Find the voltage V and the power absorbed by the 12-ohm resistor.
http://i.imgur.com/xCTEI.png

Homework Equations

p = vi
v = ir
KVL
KCL

The Attempt at a Solution

Tried using KVL and KCL in various ways. This book gives horrid examples.

 

[xcvxcvvc]

Homework Statement

Find the voltage V and the power absorbed by the 12-ohm resistor.
http://i.imgur.com/xCTEI.png

Homework Equations

p = vi
v = ir
KVL
KCL

The Attempt at a Solution

Tried using KVL and KCL in various ways. This book gives horrid examples.

You can solve using mesh analysis if you wanted, but I'd condense that middle branch into an equivalent resistance first.

4 + (1/3 + 1/6)^-1 = 6. Next, write the mesh loops, but leave out that first loop with the current source (but include its effects in that the current going through the 2 ohm resistor is (I_1 - 6))

 

[calcuseless]

I found the current in the last loop to be .4 A. Using V = IR to solve to get the voltage, I get 4.8 V at the 12-ohm resistor. I then used P = VI to get a power of 9.6 W, but the book has 1.92 W. Did I do anything wrong or is the book wrong again?

 

[xcvxcvvc]

I found the current in the last loop to be .4 A. Using V = IR to solve to get the voltage, I get 4.8 V at the 12-ohm resistor. I then used P = VI to get a power of 9.6 W, but the book has 1.92 W. Did I do anything wrong or is the book wrong again?

The current is $$.4$$ and the voltage is $$4.8$$. However, $$.4 \times 4.8$$ is not $$9.6$$. It's $$1.92$$(as the book says). Also, $$I^2 r = (.4)^2 12 = 1.92$$ as well if you wanted to avoid that extra calculation of voltage.

To see where the current-dependent equation comes from notice:
$$P=IV$$
and
$$V=IR$$
substituting $$IR$$ for voltage into the power equation brings us to:
$$P = I (IR) = I^2R$$

 

[satchmo05]

Yes, like xcvxcvvc said: P is equal to I²*R as well as V²/R. These only work when you're finding the power absorbed by the resistor! Also, I think the easiest way to solve this (because mesh equations can get ridiculous and tedious after a while --> source transformation, if you have learned it!