Question

An electric motor operates on 50V supply and a current of 12A .If the efficiency of the motor is 30% .What is the resistance of winding of the motor ?
A) $6\Omega $
B) 4$\Omega $
C) $2.9\Omega $
D) $3.1\Omega $

Answer 1

Hint:An electric motor is an electrical machine that converts electrical energy into mechanical energy .Most electric motors operate through the interaction between the motor’s magnetic field and electric current in a wire winding to generate force in the form of torque applies on the motor’s shaft.
We will find the output power first and then losses .Using the losses we will calculate the value of resistance . Let’s discuss the formula for efficiency and losses.
$\eta = \dfrac{{output}}{{input}}$
Losses = input power- output power
Losses $ = {I^2}R$

Efficiency of an electric motor is given by:
$\eta = \dfrac{{output}}{{input}}$
And losses in the motor are given by :
Losses = input –output
Complete step by step solution:
Let’s calculate the input supplied to the motor first:
Input power $ = V \times I$
    $
   = 50 \times 12 \\
   = 600VA \\
 $
Now , calculate the output power using efficiency formula

$
  input - output \\
   \Rightarrow 600 - 180 \\
   \Rightarrow 420VA \\
 $
Losses generally occurs in the winding of the rotor and armature due to the flow of current in the windings and the losses are given by :
${I^2}R = losses$ (where , I is the current given and R is the resistance of the winding which we have to find out )
$
   \Rightarrow {(12)^2} \times R = 420 \\
   \Rightarrow R = \dfrac{{420}}{{12 \times 12}} \\
   \Rightarrow R = \dfrac{{420}}{{144}} \\
   \Rightarrow R = 2.9\Omega \\
    \\
 $
Thus, the resistance of the winding is $2.9\Omega $

Option C is correct.

Note:
Electric Motors are of different types :
-Three phase motors and single phase motors
-Synchronous motors, induction motors
-DC motors and AC motors

Various uses of the motors are :
-DC motors are generally used for traction purposes( trains).
-Induction motors are mostly used in industries for production and manufacturing.
-Synchronous motors are used for power factor improvement.