Question

In a motor, a rotor is fitted with the armature that has current of 10A. The rotor rotates with the angular speed of 3rad/s. Magnetic field of magnitude 2T varies in the direction in such a way that it is always perpendicular to the loop area. If the rotor coil has N number of turns and area of each loop is $0.45m^2$ then find the value of N. Given that motor consumes 2106 W power there are no losses.

Answer 1

Hint: This is the question from the electromagnetic induction chapter. We have to find the number of turns off in the coil giving the question. Which way will we be able to find if we are able to derive a relation between the number of turns of a coil and the power consumed by the coil


Complete step by step answer:
We know the relation between Power current and the voltage. If we are able to find out the voltage across the motor armature, we will be able to find the EMF induced. Therefore, the EMF induced can be found by the following relation:
$$\begin{gathered} P=VI \\ V={\displaystyle \frac{P}{I}} \end{gathered}$$
 If we put the values of I as 10A and power as 2106 W, we get the value of the voltage:
$$\begin{gathered} V={\displaystyle \frac{2106}{10}} \\ ⟹V=210.6V \end{gathered}$$
This voltage will be equal to the EMF induced across the armature of the motor. And the relation of the EMF induced in a coil is given as:
$EMF=NBA\omega$
In which N is the number of turns, B is the magnetic field, A is the area of the armature and $\omega$ is the angular velocity.
Putting these values in the relation we can calculate the values of N.
$$\begin{gathered} EMF=NBA\omega \\ ⟹210.6=N\times 2\times 0.45\times 3 \\ ⟹N={\displaystyle \frac{210.6}{2\times 0.45\times 3}} \\ \therefore N=78 \end{gathered}$$

Hence, the number of turns in the armature of the coil is 78.


Note:
 This is a question in which two concepts are applied: one is the relation between the power current and the voltage. And the other is the EMF induced in a coil. Such questions require understanding about the relation between the formulas of two concepts. To solve such questions where there is more than one concept to apply the student should be thorough in the chapters.