Can't find the correct power of this circuit -- Please help

[tonlika]

This is the circuit:

I have found all the currents and voltages with the Kirchoff's laws. I think they are correct because they perfectly matched the results of a QUCS simulation of the circuit.

I1 = -2.241
I2 = 0.759
I3 = -0.284
I4 = 1.957
I5 = -0.241
I6 = -1.284

V(R1) = I1*R1 = -2.241 * 1 = -2.241 V
V(R3) = I2*R3 = 0.759 * 5 = 3.795 V
V(R4) = I4*R4 = 1.957 * 4 = 7.828 V
V(R5) = I5*R5 = -0.241 * 3 = -0.723 V
V(R6) = I3*R6 = -0.284 * 8 = -2.272 V
V(R7) = I6*R7 = -1.284 * 9 = 11.556 VThis is how I calculated the powers:P(R1) = I12 * R1 = 5.02 W
P(R3) = I2¬¬2 * R3 = 2.88 W
P(R4) = I42 * R4 = 15.32 W
P(R5) = I52 * R5 = 0.17 W
P(R6) = I32 * R6 = 0.65 W
P(R7) = I62 * R7 = 14.84 W
-------------------------------------
Power consumed = 38.88 WP(E1) = I1*E1 = -2.241 * 8 = -17.93 W
P(E5) = I5*E5 = -0.241 * 15 = -3.62 W
P(E6) = I3*E6 = -0.284 * (-1) = 0.284 W
P(J2) = (V2 - V3)*J2 = (6.514 + 11.556)*3 = 54.21 W
P(J8) = (V4 - 0)*J8 = 2.720 * (-1) = -2.720 W
---------------------------------------------------------------------
Power produced = 30.224 W
As you can see the power consumed doesn't equal the power produced.
What am I doing wrong?

Thanks in advance!

 

[berkeman]

This is the circuit:

I have found all the currents and voltages with the Kirchoff's laws. I think they are correct because they perfectly matched the results of a QUCS simulation of the circuit.

I1 = -2.241
I2 = 0.759
I3 = -0.284
I4 = 1.957
I5 = -0.241
I6 = -1.284

V(R1) = I1*R1 = -2.241 * 1 = -2.241 V
V(R3) = I2*R3 = 0.759 * 5 = 3.795 V
V(R4) = I4*R4 = 1.957 * 4 = 7.828 V
V(R5) = I5*R5 = -0.241 * 3 = -0.723 V
V(R6) = I3*R6 = -0.284 * 8 = -2.272 V
V(R7) = I6*R7 = -1.284 * 9 = 11.556 V


This is how I calculated the powers:


P(R1) = I12 * R1 = 5.02 W
P(R3) = I2¬¬2 * R3 = 2.88 W
P(R4) = I42 * R4 = 15.32 W
P(R5) = I52 * R5 = 0.17 W
P(R6) = I32 * R6 = 0.65 W
P(R7) = I62 * R7 = 14.84 W
-------------------------------------
Power consumed = 38.88 W


P(E1) = I1*E1 = -2.241 * 8 = -17.93 W
P(E5) = I5*E5 = -0.241 * 15 = -3.62 W
P(E6) = I3*E6 = -0.284 * (-1) = 0.284 W
P(J2) = (V2 - V3)*J2 = (6.514 + 11.556)*3 = 54.21 W
P(J8) = (V4 - 0)*J8 = 2.720 * (-1) = -2.720 W
---------------------------------------------------------------------
Power produced = 30.224 W



As you can see the power consumed doesn't equal the power produced.
What am I doing wrong?

Thanks in advance!

Should both current sources be sinking power instead of supplying it? It looks like you have one of them doing that, but not both.

 

[tonlika]

I don't understand! Please can you explain? And why should be both current sources sinking power?

 

[jegues]

I don't understand! Please can you explain? And why should be both current sources sinking power?

He's asking you a question.

Should a current source be supplying power, or dissipating (sinking) power?

 

[tonlika]

I don't know. The exercise says nothing about it. I guess they should be supplying.

 

[jegues]

I don't know. The exercise says nothing about it. I guess they should be supplying.

Well think about it, if I have circuit with a source (be it current or voltage) and one resistor, would you expect the source to be supplying power and the resistor sinking power, or vice versa?

 

[tonlika]

Well think about it, if I have circuit with a source (be it current or voltage) and one resistor, would you expect the source to be supplying power and the resistor sinking power, or vice versa?

Well, I think the source would be supplying power and the resistor sink it.

 

[jegues]

Well, I think the source would be supplying power and the resistor sink it.

Good! Now the same thing should apply to your circuit, correct?

 

[tonlika]

Good! Now the same thing should apply to your circuit, correct?

Yes, I think.

 

[berkeman]

I don't understand! Please can you explain? And why should be both current sources sinking power?

There was a thread a little while back where how to handle the power balance equations with current sources was discussed. Look for where ideasrule comes into the thread at post #16:

https://www.physicsforums.com/showthread.php?p=3281983&posted=1#post3281983

 

[jegues]

There was a thread a little while back where how to handle the power balance equations with current sources was discussed. Look for where ideasrule comes into the thread at post #16:

https://www.physicsforums.com/showthread.php?p=3281983&posted=1#post3281983

The current source's power is actually negative. The voltage sources contribute positive power because they take electrons at low potential and raise them to a higher potential, which injects energy into the circuit. On the other hand, the current source takes electrons at high potential and drops them to a lower potential, which uses power for the same reason that a voltage drop across a resistor means the resistor uses power.

You should get consistent values after addressing these two issues.

Wow, I'm fairly certain I remember doing problems similar to this demonstrating that power is conserved throughout the circuit with the current sources supplying power.

In fact my old textbook lists the conservation of power as follows,

\Sigma P_{sources} = \Sigma P_{other elements}

this is listed for both average power and complex power.

Is this incorrect?

Very interesting.

Sorry to the OP if I have been misleading.

 

[berkeman]

I don't know either. As you can tell from that thread, I was confused as well.

For the real circuits that I design, both voltage and current sources supply power. But I kept getting the wrong answers in that other thread...

 

[tedbradly]

Ideally, a voltage or current source and dissipate power. Take as an example a resistor with a the positive terminals of a 5v and 10v battery on each side. The voltage source with lower voltage dissipates power (equal to (10-5)/r*5 )

 

[gneill]

I have found all the currents and voltages with the Kirchoff's laws. I think they are correct because they perfectly matched the results of a QUCS simulation of the circuit.

<snip>

I1 = -2.241
I2 = 0.759
I3 = -0.284
I4 = 1.957
I5 = -0.241
I6 = -1.284

I thought I'd analyze the given circuit myself to confirm the current and voltage values. I'm not getting the current values that you've given. Thinking that I might have mucked up the math somewhere, I threw the circuit at a spice simulator. Spice agreed with my calculations.

Is it possible that your values for the currents correspond to a slightly different circuit somehow? Are all the sources in their specified orientations with their specified values?

For the record, the currents that I calculated which correspond to those you've indicated on your diagram:

I1 = -0.448 A
I2 = 2.552 A
I3 = 0.058 A
I4 = 0.505 A
I5 = 1.552 A
I6 = -0.942 A

Perhaps someone else can confirm?

 

[uart]

Either ideal sources, both current and voltage, can sink or source power. Think of a battery, it can supply power (discharge) or it can absorb power (recharge).

 

[tonlika]

I thought I'd analyze the given circuit myself to confirm the current and voltage values. I'm not getting the current values that you've given. Thinking that I might have mucked up the math somewhere, I threw the circuit at a spice simulator. Spice agreed with my calculations.

Is it possible that your values for the currents correspond to a slightly different circuit somehow? Are all the sources in their specified orientations with their specified values?

For the record, the currents that I calculated which correspond to those you've indicated on your diagram:

I1 = -0.448 A
I2 = 2.552 A
I3 = 0.058 A
I4 = 0.505 A
I5 = 1.552 A
I6 = -0.942 A

Perhaps someone else can confirm?

Thanks for the reply but I solved it. When I calculated the power of the sources I didn't take into account the direction of the current relative to the polarity of the source. Doing that, I found that the total power of all sources is -38.88 W so the problem is solved.

Also I must apologize to you. It is my fault to maybe have created confusion because there is a mistake in the circuits schematics. The node numbered 3 should be where the node number 4 is and vice-versa. Also I forgot to write the voltages of the nodes 1, 2, 3 and 4.

Thanks to all for your time and patience!

 

[uart]

Thanks for the reply but I solved it. When I calculated the power of the sources I didn't take into account the direction of the current relative to the polarity of the source.

Yes I was thinking that E6 and J8 might have been causing you that particular problem. Remember that there's no law to stop you from reversing the reference polarity and negating the value of a source before you start, if you wish. Personally I always redraw and negate negative valued sources that way. I see this as kind of analogous to carrying a double negative throughout a long an complicated mathematical calculation. If you don't make any mistakes then it shouldn't effect the results, but it still makes a lot more sense to just get rid of any double negative at the get go.