I have purchased four 100W (120V rated) incandescent light bulbs..?

Question

The resistance of these incandescent light bulbs was 8.90 ohms on the average (+/- 0.251 ohms if you want to split some hair):
a) How much current will the bulb consume on the average if I plug it in a 120 V circuit?
b) How much current will the bulb consume in a 12.0V circuit?
(Values are in RMS)
How do I do this problem?

Wiki eloquently states “Incandescence is the release of electromagnetic radiation, usually visible radiation, from a body due to its temperature.” This is the key to the question asked. It is not evident right the way however some of you were quick to point out that 8.90 ohms does not work well in P=V^2/R. R (@120V, 100W)=144 ohms, a 1:16 ratio between cold and hot filament [3]. The question is what makes the resistance rise and remain at that fixed level in our case that being 144 ohms. We have to consider black body (BB) radiation P=ebA(T^4 – Tc^4)
P - Power radiated
e- BB emissivity( 0 b- Boltzmann’s constant = 5.670 400(40)×10−8 W/(m^2•K^4).
A – area trough which BB radiates
T- temperature of BB
Tc – temperature of the environment BB radiates

References
1. About incandescent light bulb http://physicsed.buffalostate.edu/pubs/TPT/TPTDec99Filament.pdf
2. The physics of an incandescent bulb http://www.sci-ed-ga.org/modules/materialscience/light/
3. Linear relationship between temperature and resistance http://www.sci-ed-ga.org/modules/materialscience/light/pdf/section_08.pdf
4. Key black body radiation and ... http://www.millersville.edu/~physics/exp.of.the.month/51/

Answer 1

use ohm's law

E = IR

E = volts
I = current
R = resistance

Answer 2

You might have already noticed that the measured resistance of your light bulbs is a lot lower than the 144 ohms expected from the voltage and wattage rating. I was puzzled at first when I discovered the same thing many years ago.

The answer to this paradox is that the resistance of the light bulbs at low voltage has been accurately measured but as the filament heats up, its resistance increases, in this case by a factor of about 16 between room and operating temperature of about 3,000 deg K. When you first turn on the light, it does indeed draw a large surge of current that quickly decreases to the operating current after a fraction of a second. This is why switches sometimes have a separate, lower current rating for operating incandescent lights.

The answer to your problem is therefore this:

a) at nominal rated voltage, your bulb will consume the nominal rated power; the resistance measurements of the filament at room temperature don't apply. The RMS current can therefore be computed from the equation

I = P / V, for a current of 0.83 amps.

b) At 12.0 volts, the filament will dissipate enough power to heat up significantly and raise the resistance noticeably but nothing like the factor of 16 that occurs at full operating voltage. The current will therefore be less than 12.0 V / 8.9 Ω
or 1.35 amps but a lot more than the 0.083 amps you would expect if the light offered the same resistance it did at full working voltage. My seat-of-the-pants estimate would be a current draw in the range 0.2-0.4 amps based on my somewhat limited experience with incandescents.

Do try this at home.

Answer 3

A simple way is to use the formula I=P/V (transposed from P=I*E). So 100/120=0.833 Amperes (per bulb). But that would ignore your figures. So using your figure of 8.9 ohms and the formula I=E/R, 120/8.9=13.483 Amperes. Also, for 12 Volts, 12/8.9=1.348 Amperes.
Why the anomaly? In real life, the resistance is not constant with temperature. With metal filaments the resistance rises with temperature. Hence the difference.

Answer 4

Yes. adding up all the power gives 3450 W total. using P=VI we find, 3450 = 120I I = 28.75 A when the current rating of a fuse is exceeded it breaks the circuit. The total current of the circuit exceeds 20 A and the fuse will blow.

Answer 5

First, please understand the difference between hot and cold resistance. To get the current used, your resistance has to be the hot resistance. Voltage in RMS/hot resistance = current. Second. The bulb will give a different hot resistance when activated by 12 volts. You must know this resistance because the tungsten filament is a non linear resistance and the 12 hot will be closer to the cold resistance.

Answer 6

Of Course Raffaele1111 is right!

Answer 7

(a)
Current = Power/Voltage = 0.83 Ampere

(b)
The resistor is metallic tungsten. Its rsistance depends on temperature.
http://hypertextbook.com/facts/2004/DeannaStewart.shtml

So we need to estimate temperature of the whicker, when the bulb is plugged into 12V circuit. Lets assume for the lack of better information that all loss of heat is due to black body radiation.

Resistance of the whisker under normal operating conditions is
R(T_norm) = U²/P = 144 Ω
Which means that
R(T_norm)/R(T_room) = 16.2

Assuming that room temperature is T_room = 300K, high resistance corresponds to T_norm = 3000K according to the table.

Now we know power radited by the whisker:
P(T) = (T/T_norm)^4 x P_norm

So we need to solve equation
P(U) = U²/R(T) = (T/T_norm)^4 x P_norm

Lets make simplifying approximation of linearity of R(T):
R(T) = αT

Then
U²/(αT)= (T/T_norm)^4 x P_norm
U² = αT³ /T_norm^4 x P_norm=
T = ³√[T_norm^4/α x U²/P_norm]

R(U) = α ³√[T_norm^4/α x U²/P_norm]
I(U) = U/ ³√[T_norm^4 α² U²/P_norm]

Finally we see that power is proportional to U^(1/3). So the answer is

Current at voltage U is about I_norm x ³√(U/Unorm) ~ 0.4 A


>How do I do this problem?
Use ammeter

Answer 8

Edward,

Great question--I'd give it two stars if I could--and multiple good answers. Nothing more to add.

Answer 9

a) R=P/I^2
R=8.9/144000
R=6.18 ohms
b) 0.061 ohms

I'm not sure it would be the right way to do it.

Edit:

Oops, what a silly answer, you are looking for current...Current!
Oh well, at least now I am sure this is not the right way to do it.

I would like to thank the kind people whom gave a blind thumb up to this totally ridiculous answer...I suspect the members of the chocolate cult.

Answer 10

Wow!!!!!!

I am amazed at all the formulas

The only and proper formula is as follow hereto

V/W=A

V=volts
W=watts
A=amperes

With amperes been the Amp per hour used.

Then one needs to

A*X*Y=$

A=amperes
X=power per hour charges
Y=total hours used per usage
$=total costs per usage