Car batteries are often rated in "ampere-hours" or A*h. a.) Show that A*h has units of charge and that the value of 1 A*h is 3600 C. b.) A fully charged, heavy-duty battery is rated at 100 A*h and can deliver a current of 5.0 A steadily until depleted. What is the maximum time this battery can deliver current, assuming it isn't being charged? c.) How much charge will the battery deliver this time?

a) See below

b) 20 hours

c) 360,000 C

Explanation:

a)

Car batteries are often rated in

"Ampere-hours"

Which is written as

A*h (1)

Where:

A is the Ampere, the units of measurement of the current intensity. Since current is defined as

where q is the charge (measured in Coulombs) and t is the time (in seconds), this means that 1 Ampere is

(2)

Moreover, h is the hour, the units of measurement of the time (1 hour = 3600 seconds), therefore

(3)

Substituting (2) and (3) into eq.(1), we find that:

b)

We know that the relationship between current intensity and charge is

where:

I is the current intensity

q is the charge delivered

t is the time elapsed

For the battery in this problem, we have:

q = 100*h is the total charge delivered

I = 5.0 A is the current delivered

Therefore, solving for t, we can find the time the battery delivers this current:

So, 20 hours.

c)

In this problem, we said that the charge of the battery is rated as

Q = 100 A*h

We want to convert this charge in SI units (Coulombs).

According to what we found in part a), we can use the conversion factor

To rewrite the charge of this battery in Coulombs; we get:

Therefore, the total charge delivered by the battery during the 20 hours at 5.0 A of current is 360,000 C.