Question

One kilowatt is approximately equal to _____ hp.
A.1.34
B.1.56
C.2.50
D.1.83

Answer 1

Hint: Recall the concept of power. Recall the units of power in different systems of units. Use the conversion factor between the units of power which are kilowatt and horsepower.

Complete step by step answer:
Power is the ratio of energy with time which means the energy consumed by the object or machine in the unit time.
The SI system of power is watt (\[{\text{W}}\]).
One kilowatt power is equal to 1000 watt.
Hence, the relation between the units watt and kilowatt is
\[1\,{\text{kW}} = {\text{1000 W}}\]
Horsepower is another unit of power. The unit horsepower can be related with the watt as
\[1\,{\text{hp}} = 746{\text{ W}}\]
Hence, one horsepower is equal to 746 watt.
Calculate the number of horsepower units in the power one watt.
One watt is equal to \[\dfrac{1}{{746}}\,{\text{hp}}\].
\[1\,{\text{W}} = \dfrac{1}{{746}}\,{\text{hp}} = 0.00134\,{\text{hp}}\]
Hence, one watt power is equal to \[0.00134\,{\text{hp}}\].
Now determine the number of horsepower in one kilowatt power.
\[1\,{\text{kW}} = \left( {1000\;{\text{W}}} \right)\left( {\dfrac{1}{{746}}\,{\text{hp}}} \right) = 1.34\,{\text{hp}}\]

Therefore, one kilowatt power is equal to \[1.34\,{\text{hp}}\].

So, the correct answer is “Option A”.

Additional Information:
The various units of power are used in various applications.
The unit of power watt is used to explain power in components like bulbs.
The unit of power is used to denote the power of car, bikes, various automobiles or industrial machines.

Note:
Two different units of the same physical quantity have the same dimensions. One can also check that the dimensions of the units watt and horsepower is \[\left[ {{M^1}{L^2}{T^{ - 3}}} \right]\]. Hence, it can be proved that the dimensions of watt and horsepower are the same and so they are units of the same physical quantity i.e. power.