A constant current of 3A for 4 hours is required to charge an automotive battery. If the terminal voltage is 10 + t/2 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.

Respuesta :

A. The charge (Q) transported can be calculated using the formula Q = I * t, where I is the current and t is the time. In this case, Q = 3A * 4hr = 12Ah.

B. The energy expended (W) is given by the equation W = Q * V, where Q is the charge and V is the voltage. The voltage function is given as V = 10 + t/2. You need to integrate this function over the given time period (0 to 4 hours) to find the total energy expended.

C. To calculate the cost, convert the energy expended (in kilowatt-hours) and multiply it by the electricity cost per kilowatt-hour. Cost (C) = (W in kWh) * (cost per kWh). Ensure you convert the units appropriately.

For specific numerical results, you would need to substitute the values into the expressions.