Question

An electric motor driven pump fills an overhead tank placed at a height of 20 m from the ground-level sump at a rate of 20,000 litre water per hour.The motor has an operating resistance of $22\Omega$ and is connected across a 220 V source.The efficiency of this motor is (Use$g=9.8m/s^2)$

• A. $12.5\%$
• B. $73.5\%$
• C. $49.5\%$
• D. $22.5\%$

Answer 1

The correct option is C $49.5\%$

Rate of volume of water $V=20000\frac{\text{litre}}{h}=20000\times \frac{{10}^{-3}}{3600}\frac{m^3}{s}=\frac{20}{3600}\frac{m^3}{s}$
Mass of water pumped per second $m=\rho V=1000\times \frac{20}{3600}kg$
Input power of motor $P_{in}=\frac{V^2}{R}$
$\therefore$ $P_{in}=\frac{(220{)}^2}{22}=2200W$
Output power $P_{out}=mgh=(1000\times \frac{20}{3600})\left(9.8\right)\left(20\right)=1088.89W$
Thus efficiency $\eta =\frac{P_{out}}{P_{in}}=\frac{1088.89}{2200}=0.495=49.5$%