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  #1  
Old 06-10-2007, 02:21 PM
NichA NichA is offline
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Default Help me calculate the power developed by this simple circuit.

Homework question: Find the total energy developed in the circuit.



The first thing I need help understanding is: is this question supposed to be asking for power instead of "energy." How can you calculate the energy developed without some type of time constraint?

Ok, so assuming we are talking about power developed, here is what I know:

First, I know that i = -8 A so the dependent current source is always equal to -24 A.

Second, I must calculate the power absorbed by each element by using the formula I*V. (Of course we will use the formula -I*V if the current is moving in the direction of the voltage rise). So the power absorbed by the 20V voltage source and the 100V voltage source is -160 Watts and -1600 Watts. And since these numbers are negative that tells us that power is being delivered.

So I figured out that these two elements are developing 1760 W of power, but I can't find the power created or absorbed by the current sources because I can't create 3 independent equations to find the three remaining voltages across the terminals of the current sources. (KVL only yield two such equations)

How do I find the power absorbed or delivered by these 3 remaining circuit elements?

P.S. the answer key says the answer is 220 W so I know my answer of 1760 W is already way off!
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  #2  
Old 06-10-2007, 02:28 PM
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hgmjr hgmjr is offline
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One thing you can say with certainty is that with the answer key stating the answer in terms of Watts then your initial question is answered outright.

hgmjr

Last edited by hgmjr; 06-10-2007 at 02:33 PM.
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  #3  
Old 06-10-2007, 02:29 PM
NichA NichA is offline
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Quote:
Originally Posted by hgmjr View Post
One thing you can say with certainty is that with the answer key stating the answer in terms of Watts then you initial question is answered outright.

hgmjr
haha... good point.
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Old 06-10-2007, 02:56 PM
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hgmjr hgmjr is offline
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Since power is additive and always a positive quantity, then I am at a loss as to how the answer can be 220 Watts since you already have 1760 Watts. This is well in excess of the value given in the answer key.

Either I have overlooked something or the answer in the answer key is for a different problem or the circuit as drawn has an error.

hgmjr
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  #5  
Old 06-17-2007, 05:25 AM
Ratch Ratch is offline
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NichA,

I would say that no power is dissapated in the circuit because no resistance exists. Please post the solution when you receive it. Ratch
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  #6  
Old 08-02-2011, 09:05 AM
Laralike Laralike is offline
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I don't suppose the thing that says 3i is in fact a 660V source?
Try that.
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Old 08-02-2011, 10:59 AM
t_n_k t_n_k is offline
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I would assume there are an infinite range of possible circuit conditions but the nett energy loss is always zero.

Assume any voltage from +∞ to -∞ across the 3i controlled source and you have always have power balance as the voltage magnitude increases with either polarity.

Take the case of +20 volts across the controlled source.

The 8A source would have zero voltage drop and the 16A source would have -80V drop.

Source Powers in that case

20V source = +160W [supplying power]
100V source = +1600W [supplying power]
8A source = 0 W
16A source = -1280W [absorbing power]
Controlled source = -480W [absorbing power]

So the total power input balances the total absorbed power.

Take the case of -50V across the controlled source.

The 8A source would have -70V drop
The 16A source would have -150V drop

Source powers in that case

20V source = +160W as always
100V source = +1600W as always
8A source = -560W
16A source = -2400W
controlled source = +1200W

Once again the supplied & absorbed powers balance.

Seems a rather pointless question.
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Old 08-03-2011, 11:17 AM
t_n_k t_n_k is offline
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Perhaps a final comment ....

Imagine a very high resistance value shunting the controlled source. Let's say it's 100MΩ.

No current would flow in this resistor since the controlled source just balances the total independent current source output. By the same reasoning the shunting resistor would add no power loss to the system.

Given there is no current then there would be zero voltage drop across the resistor. So the controlled source potential difference would be zero. The controlled source would neither absorb or generate any power.

In that case the two independent current sources would absorb the 1760W derived from the two independent voltage sources. No other losses would need explanation since none would exist.

One can probably equally well reason that the shunting resistor could be any value (including 0Ω ...?) and there would be no power loss due to the presence of the resistor, irrespective of its ohmic value.

The proposed answer alluding to the mysterious & unaccounted loss of 220W continues to puzzle me. One could, for instance, place a resistance of 0.382 ohms in series with the controlled source and thereby produce the required 220W.

I wonder if the OP has inadvertently omitted any circuit elements in transcribing the schematic...?

Last edited by t_n_k; 08-03-2011 at 11:44 AM.
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  #9  
Old 08-03-2011, 04:35 PM
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AFAIK an ideal current source has zero volts across it. Thus the left leg has 20V across it, and the middle leg has 100V across it.

But as these two legs are in parallel, there cannot be two different voltages.

Thus the question is in error in at least 2 places.

Addendum: Power in watts is equivalent to joules per second. Joules is energy. One *could* ask how much energy does it consume/emit in some given time. But without specifying how much time then the energy is indeterminate.
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  #10  
Old 08-03-2011, 09:51 PM
t_n_k t_n_k is offline
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Quote:
Originally Posted by ErnieM View Post
AFAIK an ideal current source has zero volts across it.
That's incorrect.

Imagine an ideal current source of 1A driving a 1Ω load. The source has 1V across it. An ideal current source adjusts its terminal voltage to keep the current in the load constant.

Last edited by t_n_k; 08-04-2011 at 04:56 AM.
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