assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charged the battery

The amount of water that will power a battery with that rating = 7.35 m³

Explanation:

The power rating for the battery is missing from the question.

Complete Question

Assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charged the battery with power rating, 12 V, 50 Ampere-minutes

Solution

Potential energy possessed by water at that height = mgH

m = mass of the water = ρV

ρ = density of water = 1000 kg/m³

V = volume of water = ?

g = acceleration due to gravity = 9.8 m/s²

H = height of water = 50 cm = 0.5 m

Potential energy = ρVgH = 1000 × V × 9.8 × 0.5 = (4900V) J

Energy of the battery = qV

q = 50 A.h = 50 × 60 = 3,000 C

V = 12 V

qV = 3,000 × 12 = 36,000 J

Energy = 36,000 J

At a 100% conversion rate, the energy of the water totally powers the battery

(4900V) = (36,000)

4900V = 36,000

V = (36,000/4900)

V = 7.35 m³

Hope this Helps!!!