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In a circuit that is fitted with a bulb, which is the factor that affects brightness of that bulb: current in the circuit or the voltage offered by the battery in that circuit?

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which is the factor that affects brightness of that bulb, current in the circuit or the voltage

Both. It's the power that ultimately causes the filament to get hot and emit visible black body radiation.

Power is voltage times current, so both matter.

However, you can only control one degree of freedom. The bulb dictates the other. This single degree of freedom can be expressed various ways. Two of them are fixing the current and fixing the voltage. Once you fix one of these, the resistance of the bulb implicitly fixes the other.

Note that the resistance of a bulb varies considerably with temperature. It is much higher when the bulb is emitting light than when it is sitting cold and unpowered. However, that still doesn't let you fix both independently. It only means that the relationship between voltage and current changes with the set point.

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  • $\begingroup$ ...but if you increase the voltage to a bulb, it gets brighter... $\endgroup$ Jun 19, 2022 at 23:49
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If you think of the lighting element, which may be a length of tungsten or the like, as a fixed resistor of R ohms, the current in the resistor is determined by:

$$ v = R~ i, $$

Ohm's Law. The higher the voltage v the higher the current. If the brightness is caused by a flow of electrons through the filament, a higher voltage will--all things being equal-- drive more electrons to flow through the filament.

So the brightness is a function of both current and voltage, and can be said to depend on both. That is, we can write $v(i) = R~i$ or $i(v)=v/R.$

We might be tempted to say that the intensity I of the light is proportional to current, $I \propto i $ but we would have to remember that $i $ is a function of $v$ and put $I \propto i(v)=v/R.$

This can get arbitrarily complicated, since intensity of the light may not be proportional to current in a simple way, and the precise behavior of electrons in a circuit depends on the exact conditions and the nature of the components. For example, as comments below note, the resistance may not be constant, but may be a function of temperature.

An accessible article on how resistance may vary in a light bulb is given here. A plot of I vs. V shows that the resistance R is not in general constant. To characterize the circuit in terms of V and I you might have to solve $\frac{dv}{di}=f(i)$ or take some measurements to get a quantitative idea.

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  • $\begingroup$ Do you mean R=R(i) or R = R(v)? $\endgroup$
    – jim
    May 4, 2017 at 13:39
  • $\begingroup$ @jim: At the level of the question, I think R can be treated as a constant. So for purposes of the answer R does not depend on v or i, and I hope that my last paragraph covers the general case in which R is not constant. $\endgroup$
    – daniel
    May 4, 2017 at 13:48
  • $\begingroup$ @daniel: This assumes an incandescent bulb, where most of the work goes into heat. I'm sure there are other calculations for light-emitting-diodes, etc. $\endgroup$ May 4, 2017 at 13:52
  • $\begingroup$ @MikeDunlavey: Yes, good point. I will edit to reflect this. Well--the OP specified 'bulb'... $\endgroup$
    – daniel
    May 4, 2017 at 13:54
  • $\begingroup$ @daniel See the answer from Olin: "Note that the resistance of a bulb varies considerably with temperature. It is much higher when the bulb is emitting light than when it is sitting cold and unpowered." $\endgroup$
    – jim
    May 5, 2017 at 20:50
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I assume you consider Everything ideally in realm of Ohm's law,Also heat is converted to Light(Like old bulbs),If not, We have to then consider Variance of Resistance With temperature,But that is already discussed in other answers

So To answer your question,If you have a simple Resistance Battery circuit with Constant Resistance bulb, The only way you can change the current for Constant Resistance is by changing the voltage, So in a Way you can say That Voltage is what Changes current in Resistor,Which in turn produces more heat,Giving more light

So For such circuits,Voltage is what changes the brightness as it is proportional to intensity and intensity is Heat produces per unit area

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Or simply,if you will calculate the heat evolved by the bulb in a particular time then,the bulb which will emit large amount of energy will have more brightness as compared to other bulb with less energy emitted

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