Question

The total charge that an automobile battery can supply without being recharged is given in terms of Ampere-hours. A typical 12-V battery has a rating of 49 A · h . Suppose you forget to turn off the headlights in your parked automobile. If each of the two headlights draws 3.5 A , find out the time before your battery is "dead". Answer in units of hours. Answer in units of h

Answer 1

7 hours

Step-by-step explanation:

The total charge contained in the battery is

`Q = 49 A \cdot h`

And this is a charge, since it is a current multiplied by a time:

`Q=It`

The current drawn by each headlight (which is the charge consumed per second) is

`I=3.5 A`

Since we have two headlight, the total current drawn is

`I=3.5 \cdot 2 = 7 A`

Therefore, the total charge consumed by the two headlights each hour is

`q = I \cdot h = 7 A \cdot h`

So, the time before the battery is dead is

`t=(Q)/(q)=(49 Ah)/(7Ah)=7 h`