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%