Answer :
The energy expended in charging the automotive battery is 144 Joules.
To find the energy expended in charging the automotive battery, we need to calculate the total charge and then multiply it by the voltage.
Given:
Constant current = 3 A
Time = 4 hours
Terminal voltage = 10 + t/2 V
Calculate the total charge
The total charge (Q) is given by the formula:
Q = I * t
where I is the constant current and t is the time.
Substituting the values:
Q = 3 A * 4 hours
Q = 12 C (Coulombs)
Calculate the energy expended
The energy (E) is given by the formula:
E = Q * V
where Q is the total charge and V is the voltage.
Substituting the values:
V = 10 + t/2 V
E = 12 C * (10 + 4/2) V
E = 12 C * (10 + 2) V
E = 12 C * 12 V
E = 144 J (Joules)