Final answer:
To answer the student's questions: a) The charge transported through the battery is 43200 C. b) The energy expended can be determined by integrating the power over the charging period. c) The cost of charging can be calculated after determining the total energy used and multiplying it by the cost per kWh.
Step-by-step explanation:
The question asked involves physics concepts such as current, voltage, charge, energy, and power related to an automotive battery being charged. To address the student's multiple questions:
- Charge transported is found by multiplying current (I) by time (t), which is Q = I x t. So, the charge transported is 3 A times 4 hours, which equals 12 Ah or 43200 C (since 1 A = 1 C/s and 1 hour = 3600 seconds).
- Energy expanded is the integral of power over time, where power (P) is the product of current (I) and voltage (V). Since the voltage changes with time, one must integrate over the 4 hours. The formula for energy is E = ∫ P dt = ∫ I(V) dt = ∫ (3 A)(10 + t/2) dt over the interval from t=0 to t=4 hours.
- For the cost of charging, once we have the energy in kWh, we multiply it by the cost per kWh. Assuming electricity costs 9 cents/kWh, the total cost is found by multiplying the total energy incurred by 0.09 USD/kWh.
The provided examples from the book sections help illustrate relevant calculations and concepts for similar problems involving car batteries and electric current. However, they involve slightly different circumstances and values, so they would be referenced for explanatory purposes but the direct calculations for the student's questions would rely on the given question parameters.