A constant current of 3A for 4 hours is required to charge an automotive battery. If the terminal voltage is 10 + 1/2 t V, where t is in hours,
(a) how much charge is transported as a result of the charging?
(b) how much energy is expended?
(c) how much does the charging cost? Assume electricity costs 9 cents/kWh.
P = IV
q = dI/dt
P = dW/dt
The Attempt at a Solution
I originally thought I would need to convert the time into seconds to figure out the charge transported when solving for charge using an integral, the answer turned out to be right. However my problem comes to part b, and indirectly, c. When I was solving for work, I took the integral of power. I thought I needed to convert the voltage equation in terms of seconds so that's what I did. My answer was quite a ways off. Any help is appreciated.