The Powers Add How, Exactly?

Electricity and Magnetism Level 3

We have a 40 W 40W bulb and a 60 W 60W bulb, both rated for 120 V 120V AC supply. If we put these two together in series with a 120 V 120V supply, how much power (in Watts) does the combination consume?

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The answer is 24.

Steven Chase by Steven Chase , 37, USA

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1 solution

Chew-Seong Cheong
Sep 25, 2017

Assuming the filament of a light bulb is purely resistive, then the power rating is given by P = V 2 R P P = \dfrac {V^2}{R_P} ; ⟹ R P = V 2 P \implies R_P = \dfrac {V^2}P . Then the power of the two bulbs connected in series:

P s = V 2 R 40 + R 60 = V 2 V 2 40 + V 2 60 = 40 × 60 60 + 40 = 24 W \begin{aligned} P_s & = \frac {V^2}{R_{40}+R_{60}} = \frac {V^2}{\frac {V^2}{40} + \frac {V^2}{60}} = \frac {40\times 60}{60+40} = \boxed{24} \ W \end{aligned}

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