The charge that an electric battery can deliver is specified in ampere-hours.

Question 8

The charge that an electric battery can deliver is specified in ampere-hours.

For example, a battery of capacity 40 ampere-hours could supply, when fully charged, 0.2 A for 200 hours.

What is the maximum energy that a fully charged 12 V, 40 ampere-hour battery could supply?

A 1.7 kJ                       B 29 kJ                        C 1.7 MJ                     D 29 MJ

Reference: Past Exam Paper – June 2015 Paper 11 Q35

Solution:

Answer: C.

Power = VI

Power = Energy / time

Combining the 2 equations,

Energy / t = VI

Energy = VIt

The battery is described as ’12 V, 40 ampere-hour’.

This means that

e.m.f. V = 12 V

From the example give, 40 ampere-hours means that a current of 0.2 A can be supplied for 200 hours.

Notice that, when we take the product (0.2 A × 200 h) gives the number of ampere-hours (= 40).

But this is NOT in SI unit as hour is not an SI unit.

We know that 1 hour = 3600 s

So, 40 ampere-hours = 40 × 3600 ampere-seconds

‘Ampere-hours’ or ‘ampere-seconds’ actually represents the quantity ‘current × time’ (= It).

Energy = VIt

Energy = 12 × 40 × 3600

Energy = 1 728 000 J = 1.7 MJ