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

Answer:

7 hours

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

$t=\frac{Q}{q}=\frac{49 Ah}{7Ah}=7 h$