Total power of resistors in a circuit

[doktorwho]

Homework Statement

In this problem we are asked to calculate the total power of the resistors in the circuit below.

Homework Equations

$P=I^2R$

The Attempt at a Solution

My solution goes like this:
PT=PR1+PR2+PR3+PR4+PR5
I can find PR1 and PR5 immediately from the given current generators:
PR1=IG1^2*R1
PR5=IG2^2*R5

Since i know those powers one i don't need the current generators and can transform the right and left sides to thevenin equivalents:
Clearly
ET1=-ET2
ET1=E1=24V and RT1=R1=12Ω (i hope i got this right)

Now we can see that we have this type of situation. I transformed the resistor 3 as in the picture and can divide the circuits into 2 and the powers of the resistors will the sum of two.

I will be solving the left one:
Re=R3R2/(R3+R2)=4Ω
I=ET1/(Re+R1) = 24/18 = 4/3 A
and the power of two element are P3'+P2=Re*(4/3)^2 and that times 2 is the total power.
Something is wrong here. The result should yield 312 W and i just don't get that. What is wrong?

 

[Hesch]

PR1 and PR5 are correct.

Now, what are the voltages across R2, R3 and R4 ? ( Forget about Thevenin and so on )

 

[gneill]

I'm not liking your Thevenin equivalents. In particular, I don't like the Thevenin Resistance value. What happens when you suppress both sources in the sub-circuit that you're converting?

I also think you're missing out on further opportunities to directly calculate powers in certain resistors. You should have a formula for power when you know the voltage across a resistor, as well as one for when you know the current through it.

 

[doktorwho]

Oh, how dumb of me. I have the voltage across R2 and R4 and it's 24V for the R2 and -24 for the R4 so the voltage across R3 is -48V right? If so the formula is $P=\frac{U^2}{R}$

 

[doktorwho]

PR1 and PR5 are correct.

Now, what are the voltages across R2, R3 and R4 ? ( Forget about Thevenin and so on )

I'm not liking your Thevenin equivalents. In particular, I don't like the Thevenin Resistance value. What happens when you suppress both sources in the sub-circuit that you're converting?

I also think you're missing out on further opportunities to directly calculate powers in certain resistors. You should have a formula for power when you know the voltage across a resistor, as well as one for when you know the current through it.

Is the above corrrect?

 

[gneill]

Oh, how dumb of me. I have the voltage across R2 and R4 and it's 24V for the R2 and -24 for the R4 so the voltage across R3 is -48V right? If so the formula is $P=\frac{U^2}{R}$

Right.