Question

How much current is drawn by the motor of \[1{\rm{ H}}{\rm{.P}}{\rm{.}}\] from \[220{\rm{ Volt}}\]supply.
A. \[3.4{\rm{ A}}\]
B. \[2{\rm{ A}}\]
C. \[6{\rm{ A}}\]
D. \[12{\rm{ A}}\]

Answer 1

Hint:Power consumed by an electric motor can be expressed in terms of supply voltage and current drawn by the motor. We will utilise this relationship to find out the value of current drawn, which is given as the ratio of the power of the motor in watt to the supply voltage in Volt

Complete step by step answer:
Given:
Power of the motor is \[P = 1{\rm{ H}}{\rm{.P}}\].
The voltage of the supply is \[V = 220{\rm{ Volt}}\].
We have to find out the value of the current that has been drawn by the motor.
We know that one horsepower is equal to \[746{\rm{ Watt}}\].
\[1{\rm{ H}}{\rm{.P}}{\rm{.}} = 746{\rm{ Watt}}\]
\[746{\rm{ Watt}}\] Is the amount of power consumed by the motor during its operation.
We can write the expression for power of the motor in terms of current drawn by the motor and voltage of supplied.
\[P = I \cdot V\]......(1)
Here I am the amount of current drawn by the motor.
We are rearranging equation (1) in such a way that the value of current drawn by the motor can be obtained which will be equal to the ratio of power drawn by the motor to the voltage of the supply.
\[I = \frac{P}{V}\]
Substitute \[746{\rm{ Watt}}\] for P and \[220{\rm{ Volt}}\] for V in the above expression.
\[\begin{array}{c}
I = \frac{{746{\rm{ Watt}}}}{{220{\rm{ Volt}}}}\\
 = 3.39{\rm{ A}}
\end{array}\]
Therefore, on approximating the above obtained value of current we can say that the current drawn by the motor of \[1{\rm{ H}}{\rm{.P}}{\rm{.}}\] from \[220{\rm{ Volt}}\]supply is equal to \[3.4{\rm{ A}}\] and option (A) is correct.

Note:Do not forget to convert the value of power from horsepower into watt because all the units to be substituted in the relation of current should follow a similar system of units. Also, while converting the unit of power do not substitute \[735{\rm{ Watt}}\] for one horsepower because for electric motors \[1{\rm{ H}}{\rm{.P}}{\rm{. }} = 746{\rm{ Watt}}\].