Question #df0ef

1 Answer
Daniel W.
Aug 20, 2015

Headlights only : 6.00 hours
Parking lights only : 36.0 hours
Both together : 5.14 hours

Explanation:

It isn't clear whether you wanted to know the time of operation of just one set of lights or both, so I'll give all three options. (By the way, practically speaking parking lights aren't usually operable with headlights.)

First an assumption : the battery is a standard 12 V car battery.

All calculations require the energy capacity of the battery:
#W = ItV = 60*3600*12 = 2.59 × 10^6 J#

  • A capacity of 60 Ah means the battery can provide a current of 60A for 1 hour (which is 3600 s).

Next the combined power ratings:

  • Headlights only, #P=2*60=120 W#
  • Parking lights only, #P =4*5=20W#
  • Both, #P=120+20=140W#

Now the calculations for time to discharge the battery. For these we use #P=W/t ⇒ t=W/P#.
W is the energy capacity of the battery and P is the power rating for the lights.

  • Headlights only, #t= (2.59 × 10^6) /120= 2.16 × 10^4 s = 6.00 hours#
  • Parking lights only, #t= (2.59 × 10^6) /20= 1.30 × 10^5 s = 36.0 hours#
  • Both, #t= (2.59 × 10^6) /140= 1.85 × 10^4 s = 5.14 hours#
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