Question

The reserve capacity (RC) of a car battery is defined as the number of minutes the battery can provide \(25.0 \mathrm{~A}\) of current at a potential difference of \(10.5 \mathrm{~V}\). Thus, the RC indicates how long the battery can power a car whose charging system has failed. How much energy is stored in a car battery with an \(R C\) of \(110.0 ?\)

Short answer

Answer: The stored energy in the car battery is approximately 1,732,500 Joules.

Step-by-step solution

Write the given information

We have the following information provided: Reserve Capacity (RC) = 110.0 minutes Current (I) = 25.0 A Potential Difference (V) = 10.5 V

Calculate the power (P)

We will use the formula: P = V × I P = 10.5 V × 25.0 A P = 262.5 W

Convert RC from minutes to seconds

To calculate the energy in Joules, we need the time in seconds. RC = 110.0 minutes × 60 \frac{seconds}{minute} RC = 6600 s

Calculate the energy (E) stored in the battery

Now, using the formula E = P × t, we calculate the energy stored in the battery. E = 262.5 W × 6600 s E = 1732500 J The energy stored in the car battery with an RC of 110.0 minutes is approximately 1,732,500 Joules.