How does the change in voltage affect the brightness of a light bulb?

[05holtel]

Homework Statement

A light bulbs brightness can be measured by its power consumption. This in turn will depend on the I, V and R of the light bulb. The light bulb is rated at a power consumption of 1.0W when placed at a voltage of 6.0V. We change the battery from a 6.0V to a 3.0V one. Will the light bulb shine brighter than the previous case. What will be the current through the light bulb

Homework Equations

P=IV

The Attempt at a Solution

Is the power consumption 1.0W for both cases
If it is then I1=1/6 and I2 =1/3 Therefore the latter example will shine brighter

If not how do i take into account the changing power

 

[irycio]

It says that the power consumption is of 1 W whan placed at 6 V, not all the time. You might want to calculate, say, resistance of the light bulb (P=IU=U^2/R), what should then allow you to calculate the power consumption of the same bulb placed at 3V.

 

[xcvxcvvc]

You could also notice that
$$p \alpha V^2$$
so decreasing $$V$$ by $$\frac{1}{2}$$ decreases p by $$\frac{1}{4}$$

or you could multiply out the old $$V^2$$ and multiply the new one in:
$$p_{3V} = p_{6V}\frac{3^2}{6^2}=p_{6V}\frac{1}{4}$$