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An automobile battery is charged with a constant current of 2 A for five hours. The
Chapter 1, Problem P 1.5-5(choose chapter or problem)
An automobile battery is charged with a constant current of 2 A for five hours. The terminal voltage of the battery is v = 11 þ 0.5t V for t > 0, where t is in hours. (a) Find the energy delivered to the battery during the five hours. (b) If electric energy costs 15 cents/kWh, find the cost of charging the battery for five hours.
Questions & Answers
QUESTION:
An automobile battery is charged with a constant current of 2 A for five hours. The terminal voltage of the battery is v = 11 þ 0.5t V for t > 0, where t is in hours. (a) Find the energy delivered to the battery during the five hours. (b) If electric energy costs 15 cents/kWh, find the cost of charging the battery for five hours.
ANSWER:Step 1 of 3
From the task, we know current, dependence between voltage and time and time for battery charge.
a. We must determine energy delivered to the battery. First we will find power and after that energy which battery is used.
We know voltage v(t) in dependence to time in hours . For t > 0 we have.
For t > 0 in seconds we have:
Current is constant :
The dependence between power p(t), voltage v(t) and current i(t) is given by equation:
Now we can find power p.
