Question

A car owner forgets to turn off the headlights of his car while it is parked in his garage. If the 12.0-V battery in his car is rated at 43.0 A · h and each headlight requires 32.4 W of power, how long will it take the battery to completely discharge?

Answer 1

9.76 h.

Step-by-step explanation:

Given:

V = 12 V

I × t = 43 Ah

Power, P = 32.4 W

Assume, 2 headlights:

P = 64.8 W

Power = Energy/time

Energy = I × V × t

= 43 × 12

= 516 J

Time = 516/64.8

= 7.69 h.

Answer 2

It will take time=7.963 hours to completely discharge

Step-by-step explanation:

The energy available in the battery is:

Energy stored=Power×Time

Energy stored=(ΔV)I×t

Energy stored=(12.0V×43.0A.h)

Energy stored=516 W.h

The two headlights together consume a total power of:

`P=2*32.4W\\P=64.8W`

So the time required to completely discharge is:

`time=(Energy.stored)/(P)\\ time=(516 W.h)/(64.8W)\\ time=7.963hours`

It will take time=7.963 hours to completely discharge