Answer:
The price per kWh is [tex]c = \$ 66.67[/tex]
The energy density in watt-hours per lb is [tex]Z = 13.33 \ Wh /lb[/tex]
Explanation:
From the question we are told that
The voltage of the battery is [tex]V = 12 \ V[/tex]
The capacity of the battery is [tex]I t = 50 \ amp \cdot hour[/tex]
The price is [tex]C = \$ 40[/tex]
The weight of the battery is [tex]W = 45 lb[/tex]
Generally the energy generated by the battery is mathematically represented as
[tex]E = P * t[/tex]
Here P is power which is represented as
[tex]P = I V[/tex]
So
[tex]E = IV * t[/tex]
=> [tex]E = It * V[/tex]
=> [tex]E =50 * 12[/tex]
=> [tex]E =600 \ W h[/tex]
converting to kW h
=> [tex]E =\frac{600 }{1000}[/tex]
=> [tex]E = 0.6 \ kWh[/tex]
Generally the cost of this energy produced is [tex]C = \$ 40[/tex] Hence the cost of 1 kWh is mathematically represented as
[tex]c = \frac{C}{ E}[/tex]
=> [tex]c = \frac{40}{ 0.6}[/tex]
=> [tex]c = \$ 66.67[/tex]
Generally the energy density is mathematically represented as
[tex]Z= \frac{E}{W}[/tex]
=> [tex]Z = \frac{600}{45}[/tex]
=> [tex]Z = 13.33 \ Wh /lb[/tex]
