Bulbs connected in series power consumed

[zorro]

Homework Statement

Two bulbs which consume powers P1 and P2 are connected in series. What is the power consumed by the combination?

The Attempt at a Solution

Assuming that the same voltage is applied across the bulbs when connected separately,
R1 = V²/P1
R2 = V²/P2

When connected in series, total resistance of the circuit is V²(1/P1 + 1/P2).
So power consumed = V²/Rs = P1P2/(P1+P2)

But this is not the correct answer

 

[ashishsinghal]

Can't find anything wrong here. What is the correct answer?

 

[zorro]

P1+p2

 

[albert1993]

Draw the figure described. Assume the current flowing is A and the total voltage is V. Now the voltages in each bulb should be P1/A and P2/A. If we add we should get (P1+P2)/A = V. We are looking for Ptotal here which is VA. Thus P total = VA = P1 + P2

 

[ashishsinghal]

Now the voltages in each bulb should be P1/A and P2/A.

Here how have you taken voltage in each bulb is P1/A. Have you considered that the power of the bulb remains same. But it will not remain same.

R = V₁²/P1

Now under some other V₂

P2 = V₂²/R = V₂²*P1/V₁².
Hence these are not equal

 

[gneill]

The problem statement only states what power is consumed separately by each bulb. It makes no mention of supply voltages or currents, so any assumptions you make about either of these is going to be problematical. The minimalist, naive interpretation should be taken, namely that the power consumed by the bulbs is just what is stated: P1 and P2.

 

[zorro]

The problem statement only states what power is consumed separately by each bulb. It makes no mention of supply voltages or currents, so any assumptions you make about either of these is going to be problematical. The minimalist, naive interpretation should be taken, namely that the power consumed by the bulbs is just what is stated: P1 and P2.

What interpretation leads us to the correct answer?

 

[LareeRudi]

It's way past 2am my time; got to be short w/o giving answer. First, I don't see anybody discussing I sub 1 [amperage of first bulb], then I sub 2 [amperage of second bulb] and then of course when putting them in series, I sub 3 [same amps going thru both].

Then as to "assumptions", say they were household bulbs, or flashlight bulbs, or 12V auto bulbs. In a problem stated as it was/is, I think it is fair to assume THIS:

Both bulbs' power ratings were derived using a certain voltage; the SAME voltage for both, and THEN w/i this same problem when they are put in series, it'd not be fair to assume that they're going to throw in a DIFFERENT Voltage than the one they "started" with...

Hope it helps

LarryR : )

 

[gneill]

It's way past 2am my time; got to be short w/o giving answer. First, I don't see anybody discussing I sub 1 [amperage of first bulb], then I sub 2 [amperage of second bulb] and then of course when putting them in series, I sub 3 [same amps going thru both].

Then as to "assumptions", say they were household bulbs, or flashlight bulbs, or 12V auto bulbs. In a problem stated as it was/is, I think it is fair to assume THIS:

Both bulbs' power ratings were derived using a certain voltage; the SAME voltage for both, and THEN w/i this same problem when they are put in series, it'd not be fair to assume that they're going to throw in a DIFFERENT Voltage than the one they "started" with...

Hope it helps

LarryR : )

No, this is just assumption piled upon assumption. The problem statement makes no mention of the type of bulb, the working environment, the circuit layout, how the bulb power was determined, or anything else other than the power consumed by the bulbs. EVERYTHING else is pure conjecture.

The ONLY information you can work with is the given power ratings of the bulbs, and the only safe assumption to make is that this power consumption is their design spec. for the stated series connection.

 

[lewando]

If you make no assumptions and parse the question carefully, you will not read anything about the power ratings of the bulbs. Said bulbs "which consume powers P1 and P2" are doing exactly that--consuming powers P1 and P2. The series configuration is extraneous information.

 

[Epistemic]

Is this a complete circuit in steady state?

If so, then the current going through both bulbs is the same, I, since the bulbs are in series. Again since the bulbs are in series, you can add the resistances and get an equivalent resistance. From this we see that the voltage drop across the bulbs is <br /> V=I(R_{1}+R_{2})<br />
You then have the power in a bulb as <br /> P\ =\ V^2/R\ =\ I^2R\ =\ VI<br />

Try putting these two formulas together and see if you can't get that answer. Any of the three power formulas will work. Hope this helps.

 

[LareeRudi]

Here how have you taken voltage in each bulb is P1/A. Have you considered that the power of the bulb remains same. But it will not remain same.

...... these are not equal

I didn't do your math, but I agree that the power of each bulb does NOT stay the same as it was when installed in parallel.

Assumptions? There are times for valid assumptions. When you buy a bulb for you home, they list the "power" on the box; example 100 watts. Now that ASSUMES that you're going to put it in a normal household circuit of 110-120 volts. BUT if you put it on 72 volts [WHO DOES THAT?], so they're not being dishonest, they're advertising "normal usage".

Now when it comes to homework problems they try to get us to THINK, so tho nobody might PUT them in series, the author simply wanted us to THINK, and SEE WHAT HAPPENS.

thus, the voltage across each bulb in the beginning, is [valid assumption] goig to be the voltage across the COMBINED bulbs; that is, there is going to be an intermediate voltage between them that must be used to calculate the "new" power at that "new" voltage, not to mention, with the "new" amperage.

Thus the original P1 and P2 will NOT be the same when connected in series; I call it P3 for the first one, and P4 for the second one.

And these "new" powers will NOT match the advertised "powers"... because they are not being "used" in the "normal" way. ie, it's an "academic" question, and we allow those when we enter the field of academia.

This response is NOT necessarily only to the person I'm quoting, it's to everybody, and I just thought this was a good place to do it.

Reader's Digest version; the POWER that a bulb puts out DEPENDS on the voltage applied to it, NOT to what it says on the package.

thx,

LarryR : )

 

[gneill]

The problem statement does not state that they are household-use bulbs. It does not say anything about what type of bulbs they are, or what their normal operating voltage is (there are literally THOUSANDS of different types of bulbs with different voltage and current requirements for various purposes). The problem does not say that the series circuit involves household mains voltage. The problem does not state that the bulb power is measured under some other circuit conditions. The problem does not state ANYTHING except that the bulbs consume powers P1 and P2. Anything else you read into it is merely your own fabrication, and not supported by the problem statement as-is.

 

[LareeRudi]

The problem statement does not state that they are household-use bulbs. It does not say anything about what type of bulbs they are, or what their normal operating voltage is (there are literally THOUSANDS of different types of bulbs with different voltage and current requirements for various purposes). The problem does not say that the series circuit involves household mains voltage. The problem does not state that the bulb power is measured under some other circuit conditions. The problem does not state ANYTHING except that the bulbs consume powers P1 and P2. Anything else you read into it is merely your own fabrication, and not supported by the problem statement as-is.

I apologize if I led anybody to believe thatthe original post STATED househld bulbs; I agree, there is NOTHING in that original post that says "household" bulbs, but there is nothing in MY post that says the original post MEANT or STATED household bulbs either; it was an example of "power" is used for a bulb, and I chose to use an example that was/is FAMILIAR to most people; students or not.

So please notice that I didn't say they were. But my explanation would be valid for most types of common bulbs, regardless if they were auto bulbs, flashlight bulbs or etc... only thing is that they don't typically state the "power", thus again, I used the "household" bulbs as an example.

Stated another way, I've been scratching MY head ever since I've seen that original post. I don't even PRETEND to know the intent; just tossing out ideas.

Thus, I did NOT fabricate household bulbs into the original post; it was only itended as an example to explain my thoughts on the OP.

I apologize if I mislead anybody.

thx,

LarryR

 

[ashishsinghal]

All the arguments, however, have not led us to the answer. Hence --- Get to the point.

 

[Mark44]

In post 3, the OP says that the answer to this problem is P1 + P2. That answer seems obvious to me, considering that the two bulbs are connected in series.

 

[LareeRudi]

In post 3, the OP says that the answer to this problem is P1 + P2. That answer seems obvious to me, considering that the two bulbs are connected in series.

I don't claim to have THE answer, but have ideas.

However the "answer" of "two bulbs having power of P1 and P2, connect them in series and what is the new power"? and the answer being the same as what was GIVEN, doesn't seem to be a "problem" at all.....

There was no "homework" involved, just re-state the answer that was GIVEN... would an author or professor write a question like that?

Again, I have an idea that what was INTENDED was something like this [do we know if the OP stated it EXACTLY as it was in the book, or the exam]?:

Two bulbs that normally produce powers of P1 and P2 respectively, are now wired in series. What will be the power of each bulb NOW?

And it is NOT P1 and P2.

The amperage changes thru the bulbs when in series, compared to NORMAL installation, and thus, the I^2*R is DIFFERENT. Generally, I'll say that bulbs during "normal" use ARE wired in parallel; whether in a home, a car, or a control panel; they ALL get the full voltage provided. But when you take those same two bulbs and wire them in series, NOW the voltage across EACH bulb is no longer the "original" voltage provided, but some reduced value, depending on what the resistances are.

I've got it all worked out, but kind of lengthy for me to write out, however I'm willing; wish I knew how to upload a scan; I'd do it longhand.

LarryR

 

[LareeRudi]

In post 3, the OP says that the answer to this problem is P1 + P2. That answer seems obvious to me, considering that the two bulbs are connected in series.

Shorter version; I choose household bulbs because they are so common; take a 100 watt bulb and "install" it; P1 = 100 watts

Now take a 150 watt bulb and "install" it; P2 = 150 watts.

Now put them in series, and the total power of the bulbs is NOT P1 + P2

It's something LESS.

LarryR

 

[lewando]

There was no "homework" involved, just re-state the answer that was GIVEN... would an author or professor write a question like that?

Probably not, but I have seen ill-formed questions posed on this forum before, so I am not surprised by this one. Many possible reasons exist for their occurrence: typos, bad translation, essential information not included, or just plain bad question.

 

[ashishsinghal]

Please elaborate this obvious answer after reading the arguments above.

 

[Mark44]

Each bulb has a certain resistance, say R₁ and R₂. In a series circuit, the resistances add, so the total resistance of the two bulbs is R_Total = R₁ + R₂. Also, in a series circuit, the current I is the same through each component.

For the first bulb, the power consumed is P₁ = I²R₁, and for the second bulb, the power consumed is P₂ = I²R₂.

The power consumed in the circuit is P = I²R_Total = I²(R₁ + R₂) = I²R₁ + I²R₂ = P₁ + P₂.

When I gave my previous response, the equations above didn't go through my mind. However, I knew that if you have a device that draws, say, 1000W in a circuit, and you plug in another device that draws 1200W, the power consumed is additive, and you'll probably cause a 15A circuit breaker to trip in house with 110 V wiring (standard in the US).

 

[olivermsun]

...if you have a device that draws, say, 1000W in a circuit, and you plug in another device that draws 1200W, the power consumed is additive, and you'll probably cause a 15A circuit breaker to trip in house with 110 V wiring (standard in the US).

Are those devices usually wired in parallel, though?

 

[Mark44]

Actually, yes. After some thought, and having just finished putting in the wiring in a shed I recently bought, many of the components of an electrical circuit are wired in parallel, particularly lights. If you wire light bulbs in series, when one burns out, all of the lights go out. This was a vexing problem with Christmas tree lights some years ago.

 

[olivermsun]

i remember those Christmas lights. ;)

But yeah, for the series bulbs I kind of imagine it like this: you have V (house current or whatever you want), you have R1, R2 so that P1 = V^2/R1, P2 = V^2/R2. That's how I understand the label "75 W bulb" anyway. So now you wire them in series and you get Ptotal = V^2/(R1+R2), which has got to be smaller than either P1 or P2. I'm guessing this is what LareeRudi is thinking of as well.

If on the other hand if you think of the bulbs as "magic bulbs" which always dissipate the same power no matter what voltage or current flows through them, then R1, R2 have to change to be whatever they need to be. If so, I guess you couldn't really say anything except that Ptotal = P1+P2 no matter whether the bulbs are wired in parallel, series, or not at all for that matter.

 

[gneill]

Suppose that the problem statement did not mention bulbs but resistors instead. So the problem statement would have been:

"Two resistors which consume powers P1 and P2 are connected in series. What is the power consumed by the combination?"

Would this thread have lasted so long? Would not the argument that it doesn't matter how they're connected, if one is consuming P1 and the other is consuming P2, then together they are consuming P1+P2 have presented itself almost immediately? Isn't the detail of their fashion of connection simply superfluous information?

It seems that the word "bulb" is causing people to inject all sorts of "common sense" assumptions associated with the care and feeding of household light bulbs into the mix that are simply not present in the specific problem statement. Granted that because of this 'baiting' quality the problem might be considered to be incomplete, poorly worded, or downright evil, but in the end it may serve as a warning not to let preconceptions intrude upon unbiased analysis!

 

[olivermsun]

It would have been more clear, IMHO, because "resistors" are typically specified by a "resistance," while their power dissipation is voltage- (or current-) dependent. Hence you get all sorts of homework questions about series and parallel combinations of resistors, total resistance, current, power, etc. It would have been even more likely that how they're connected was the central point of the problem.

 

[gneill]

It would have been more clear, IMHO, because "resistors" are typically specified by a "resistance," while their power dissipation is voltage- (or current-) dependent. Hence you get all sorts of homework questions about series and parallel combinations of resistors, total resistance, current, power, etc. It would have been even more likely that how they're connected was the central point of the problem.

We can speculate unprofitably on what other problems do or don't do, or what concepts they are trying to convey, or what constitutes "usual" parameters or conditions for components, but if the whole of given problem is the statement:

"Two resistors which consume powers P1 and P2 are connected in series. What is the power consumed by the combination?"

How would one answer? Note that there is no mention of specific resistances, voltages, or currents.

 

[olivermsun]

We can speculate unprofitably on what other problems do or don't do, or what concepts they are trying to convey, or what constitutes "usual" parameters or conditions for components, but if the whole of given problem is the statement:

"Two resistors which consume powers P1 and P2 are connected in series. What is the power consumed by the combination?"

How would one answer? Note that there is no mention of specific resistances, voltages, or currents.

It does say "resistors" which implies a certain resistance, in the same way that saying "wheel" would imply a certain roundness.

Hence, a reasonable answer would be that the pair of resistors in series would consume power 1/(1/P1+1/P2) if plugged in the same voltage source where they consumed P1, P2. You could write that explicitly that in the homework solution if you were worried about the possible ambiguity, but the question as stated is basically meaningless without assuming something.

 

[gneill]

It does say "resistors" which implies a certain resistance, in the same way that saying "wheel" would imply a certain roundness.

Hence, a reasonable answer would be that the pair of resistors in series would consume power 1/(1/P1+1/P2) if plugged in the same voltage source where they consumed P1, P2. You could write that explicitly that in the homework solution if you were worried about the possible ambiguity, but the question as stated is basically meaningless without assuming something.

There is no mention of any previous connection setup. There is no mention of any "original" operating voltage, if any, that preceded the extant series connection. There is no mention of particular resistor values operating at some voltage before, and now being rearranged; No rearrangement is stated. All this is speculation and assumption being read-in where it is unwarranted! The question provides no information that would allow us to frame such assumptions with any confidence.

The only hard information given is that one resistor consumes P1 and the other P2. There is no past or future connotation; "Two resistors which consume powers P1 and P2" means that there are, now, two resistors, and one consumes P1 while the other consumes P2. Together there is P1 + P2 power being consumed. That's the long and the short of it.

I do realize that the problem just begs one to make assumptions that would actually have you answering some other, perhaps more interesting question. But sometimes one plus one really is just two, even for very large values of one.