A constant current of 2A for 30 hours is required to charge a marine battery having a voltage at its terminals of v(t) = 12(1 + e −t/30) V, where t is in hours. Assuming an electricity cost $0.20 per KWh, what is the cost to charge the battery?

$0.1584

Explanation:

Power = current×voltage

P = IV Equation 1

Where P = power, I = current, V = voltage.

V(t) = 12(1+e-t/30) Equation 2

Where t = 30 hours

Substitute into equation 2

V(t) = 12(1+e-30/30)

V(t) = 12(1+e-1)

V(t) = 12(1.1)

V(t) = 13.2 V.

also, I = 2 A.

Substitute into equation 1

P = 2×13.2

P = 26.4 W.

P = 0.0264 kW.

Energy consumed by the battery = 0.0264×30 = 0.792 kWh.

If, 1 kWh =  $0.2

Then,0.792 kWh = 0.2×0.792 = $0.1584

Hence the cost to charge the battery = $0.1584