Answer :
Final answer:
The work done when charging a 12-V automotive storage battery with 2 A for 24 hours is 2073.6 kJ. The cost of the electricity used is $0.04608, based on a rate of $0.08 per kWh.
Explanation:
To calculate the work done when charging an automotive storage battery, we use the formula Work (W) = Voltage (V) × Current (I) × Time (t). In this scenario, the battery is charged with a constant current of 2 A for 24 h at a voltage of 12 V. First, we find the work done:
W = V × I × t
= 12 V × 2 A × (24 h × 3600 s/h)
= 12 V × 2 A × 86400 s
= 2,073,600 J or 2073.6 kJ (since 1 J = 1e-3 kJ).
Next, we determine the cost of the electricity used to charge the battery by converting the work done to kilowatt-hours and multiplying by the cost per kilowatt-hour:
Energy in kWh = Work in J / (3.6e6 J/kWh)
Energy in kWh = 2073.6 kJ / (3.6e3 kJ/kWh)
Energy in kWh = 0.576 kWh
Total cost = Energy in kWh × Cost per kWh
Total cost = 0.576 kWh × $0.08/kWh
Total cost = $0.04608
Thus, the network for the cycle in terms of cost is $0.04608. Note that this is not 'network' in the physical sense, which typically refers to the work done after accounting for losses, but rather the net cost associated with the energy provided to the battery.