Lightbulb Brightness?

Question

You obtain a 90 W light bulb and a 40 W light bulb. Instead of connecting them in the normal way, i.e., in parallel across 120 V household voltage, you devise a circuit that places them in series across 120 V. Which statement is correct?

The answer is below, but I don't understand why its right.

The bulb with the smaller power rating glows more brightly than the one with the greater power rating.

Answer 1

I suspect you left some details out of the question when you posted it here.

Answer 2

R90 = E²/P = 120²/90 = 160Ω

R40 = 120²/40 = 360Ω

Series current i = E/ΣR = 120/(160+360) = .23077 amp

P40 = i²*R40 = .23077²*360 = 19.2 W W

P90 = i²*R90 = .23077²*160 = 8.5 W

So, the smaller bulb is consuming more than twice the power of the larger one.