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Practice Problems 0503 An electric motor operates a pump that irrigates a crop by pumping 10000 L of water 8 m high into a field each hour (1 L of water has a mass of 1 kg). The motor has an operating resistance of 22 ohms and is connected to a 110 V source. What current does it draw and how efficient is the motor? (answers: 5 Amps, 39.6 %) Δh = 8 m m = 10000 kg t = 1 hour = 60 minutes = 3600 seconds ∆V = 110 volts R = 22 ohms To solve for current V R 110 I= 22 I = 5 Amperes I= To solve for efficiency % efficiency = useful output E x100% input E Now lets solve for useful output E. When lifting water over a distance of 8 m, the useful output energy is GPE. ∆Ug = mg∆h ∆Ug = 10000(9.8)(8) ∆Ug = 784000 J To determine the input E P= E t But power is currently unknown, hence to determine power P = IV = 5(110) = 550 Watts Now we can continue the problem and solve for input E P= E t 660 = E 3600 550(3600) = E 1980000 J = E Finally, to solve for efficiency % efficiency = useful output E x100% input E % efficiency = 784000 x100% 2376000 % efficiency = 39.6%