Answer :
Final answer:
The cost of recharging a 12-V automotive storage battery at $0.08 per kWh over 24 hours is approximately $0.05.
Explanation:
To find the cost of recharging a 12-V automotive storage battery with a constant current of 2 amp for 24 h, we need to calculate the total energy consumed in kilowatt-hours (kWh) and then multiply it by the cost of electricity per unit. The formula for electrical energy (E) in kilowatt-hours is E = P × t, where P is power in kilowatts (kW) and t is time in hours (h).
First, let's calculate the power being used:
- Power (P) = Voltage (V) × Current (I)
- P = 12 V × 2 A = 24 W
- To convert watts to kilowatts, divide by 1000: P = 24 W / 1000 = 0.024 kW
Next, we use the time of 24 h:
- Energy (E) = Power (P) × Time (t)
- E = 0.024 kW × 24 h = 0.576 kWh
Finally, we find the cost by multiplying the energy consumed by the cost per kWh:
- Cost = Energy (E) × Cost per kWh
- Cost = 0.576 kWh × $0.08/kWh
- Cost = $0.04608
Therefore, the cost of recharging the battery at $0.08 per kWh for 24 hours is approximately $0.046. However, when rounding to the nearest cent, it costs about $0.05.
