Question:
An installation consisting of an electric motor driving a water pump left $75\, L$ of water per second to a height of $4.7\, m$. If the motor consumes a power of $5\, kW$, then the efficiency of the installation is
An installation consisting of an electric motor driving a water pump left $75\, L$ of water per second to a height of $4.7\, m$. If the motor consumes a power of $5\, kW$, then the efficiency of the installation is
Updated On: Apr 26, 2024
- 0.39
- 0.69
- 0.93
- 0.96
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The Correct Option is B
Solution and Explanation
Power consumed by the motor $=5\, kW$
$=5 \times 10^{3} W$
$=5000\, W$
Power used in lifting the water
$-\frac{m g h}{t}$
$=7.5 \times 9.8 \times 4.7$
$=3454.5\, kW$
Efficiency $= \frac{\text { Power used }}{\text { Power consumed }} \times 100 \%$
$=\frac{3454.5}{5000} \times 100=69 \%$
$=5 \times 10^{3} W$
$=5000\, W$
Power used in lifting the water
$-\frac{m g h}{t}$
$=7.5 \times 9.8 \times 4.7$
$=3454.5\, kW$
Efficiency $= \frac{\text { Power used }}{\text { Power consumed }} \times 100 \%$
$=\frac{3454.5}{5000} \times 100=69 \%$
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Concepts Used:
Electric Power
Power is defined as the rate of doing work. Electric power is the rate at which electrical energy is transferred through an electric circuit, i.e. the rate of transfer of electricity. The symbol for Electric Power is ‘P’. SI unit of electric power is Watt.
Electric Power Formula
P = VI
From Ohm's Law, V = IR
Hence, Power can also be expressed as P = I2R