Question

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?

Answer 1

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

$I=\frac{q}{t}$

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

$1A=\frac{1C}{1s}$ (2)

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

$1 h = 3600 s$ (3)

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

$1A\cdot h = (\frac{1C}{1s})\cdot (3600 s)=3600 C$

b)

We know that the relationship between current intensity and charge is

$I=\frac{q}{t}$

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:

$t=\frac{q}{I}=\frac{100 A\cdot h}{5.0}=20 h$

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

$1A\cdot h = 3600 C$

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

$Q=100 A\cdot h \cdot (3600)=360,000 C$

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