Question

Calculate the resistance offered by a 3 HP water pump which runs on 220 V supply.
A) $21.63\mathrm{\Omega }$
B) $42.6\mathrm{\Omega }$
C) $63.2\mathrm{\Omega }$
D) $37.6\mathrm{\Omega }$

Answer 1

Hint: In this question, we come across a different unit of power, i.e. Horsepower. We will convert this unit into S.I. unit. Then, we can use the formula of electric power and calculate the value of resistance offered by the water pump.

Complete step-by-step answer:
Horsepower is a unit of Electric Power.
We will initially be converting the given Horsepower into watt which is the S.I. unit of power.
$1$ horsepower $=$ $746$ watt
Therefore, $3$ horsepower $=3\times 746watt=2238watts$
Now we can use the formula for electric power(P) which is,
Electric Power $={\displaystyle \frac{\text{Potential differenc}{\text{e}}^2}{\text{Resistance}}}$
Expressing it mathematically we can write,
$P={\displaystyle \frac{V^2}{R}}$
Thus, $R={\displaystyle \frac{V^2}{P}}$
Substituting value of V and P from above, we get
$R={\displaystyle \frac{{2238}^2}{220}}$$P={\displaystyle \frac{V^2}{R}}$
$R=21.63\mathrm{\Omega }$

Hence, the correct option is option A.

Additional Information: Electric power is defined as the work done per unit time. This work is done in order to bring a charge from one point to another. The S.I. unit of Electric power is watt (W). This unit is small and is not convenient for large scale electrical energy consumption. Thus, a greater unit i.e. kW which is equal to 1000 W is used for commercial purposes. On the other hand, horsepower is a unit of electric power used for the measurement of power or the rate at which work is done, usually in reference to the output of engines or motors or pumps.

Note: Generally, the formula for electric power is written as $P=V\times I$ --[equation 1]
Now from Ohm’s Law we already know that $I={\displaystyle \frac{V}{R}}$, substituting value of I in equation 1 we get, $P=V\times {\displaystyle \frac{V}{R}}$ or $P={\displaystyle \frac{V^2}{R}}$.