# A person accidentally leaves a car with the lights on. If eachof the two headlights uses 43 W andeach of the two taillights 7.0 W,for a total of 1.0E2 W, how longwill a fresh 12-V battery last if it is rated at 8.0E1 A·h? Assume the full 12 V appears across each bulb.

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A person accidentally leaves a car with the lights on. If eachof the two headlights uses 43 W andeach of the two taillights 7.0 W,for a total of 1.0E2 W, how longwill a fresh 12-V battery last if it is rated at 8.0E1 A·h?
Assume the full 12 V appears across each bulb.

2021-05-07
P = 100W
1 A*h = 3600 A*s (Coulombs), therefore:
Q = 288000 C
E = 12 V
For a battery, P=EI.
$$\displaystyle{I}=\triangle\frac{{Q}}{\triangle}{t}$$
Transposing these equations and solving for $$\displaystyle\triangle{t}$$ the followingequation resolves:
$$\displaystyle\triangle{t}=\frac{{{E}\triangle{Q}}}{{P}}={34560}{s}={9.6}$$ hours (So that's why theyhad it in A*h originally)

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