Question

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A⋅h). A 50−A⋅ h battery can supply a current of 50 A for 1.0h, or 25 A for 2.0h, , and so on.

What total energy can be supplied by a 11 v , 40 a⋅h battery if its internal resistance is negligible?

Answer 1

The total energy that a 40 Ah, 11 V car battery can supply is calculated by multiplying the charge capacity in Ah with the voltage and then converting to joules. The resulting total energy that can be supplied is 1584000 joules.

Step-by-step explanation:

The student asked about the total energy that can be supplied by a 40 Ah battery at 11 volts with negligible internal resistance. To find this, we will use the relationship between ampere-hours and energy. Ampere-hours (Ah) give us the charge capacity of the battery, and when multiplied by voltage (V), it yields the total energy in watt-hours (Wh).

First, we convert the charge capacity from ampere-hours to ampere-seconds (coulombs), knowing that 1 Ah = 3600 As:

• 40 Ah = 40 × 3600 As = 144000 As (or coulombs).

Then, using the formula Energy (Wh) = Charge (Ah) × Voltage (V), we can calculate the total energy supplied by the battery:

• Energy = 40 Ah × 11 V = 440 Wh.

To convert this to joules, we use the conversion factor where 1 Wh = 3600 joules:

• Energy = 440 Wh × 3600 J/Wh = 1584000 J (joules).

Thus, the total energy that can be supplied by a 40 Ah, 11 V car battery is 1584000 joules.