Question

In an AC generator, the rate of change of magnetic flux through the coil is maximum when the angle between the plane of the coil is maximum when the angle between the plane of the coil and lines of force is
A. $0°$
B. $60°$
C. $30°$
D. $90°$

Answer 1

Hint: Use the formula for magnetic flux through a coil in an AC generator. Take the derivative of that formula to get the rate of change in magnetic flux. Magnetic flux through a coil is maximum when it is equal to zero. Thus, equate this equation to zero and find the angle between the plane of the coil and lines of force.

Formula used:
$Magnetic \quad flux= NABsin\phi$

Complete step by step answer:
Magnetic flux through the coil in an AC generator is given by,
$Magnetic \quad flux= NABsin\phi$
Then, rate of change of magnetic flux through the coil is given by,
$ \dfrac {d\phi}{dt}$= NAB $\omega cos\phi$
The rate of change of magnetic flux through the coil is maximum when NAB $\omega cos\phi$ is maximum. NAB $\omega cos\phi$ will be maximum when $cos\phi$ will be maximum.
$\Rightarrow cos\phi$= maximum
$\Rightarrow cos\phi = 1$
$\Rightarrow \phi= 0°$
Thus, the rate of change of magnetic flux through the coil is maximum when the angle between the plane of coil and lines of force is $ 0°$.
Hence, the correct answer is option A i.e. $0°$.

Note:
When the angle between the plane of coil and lines of force is $90°$, the maximum number of lines of force passes through the coil. These AC generators can be stepped up or stepped down using transformers. Large power AC generators are hazardous. In an AC generator for any given number of rotations induced emf remains constant and thus by applying any low resistance across the output we can generate enormous power. Generation of AC is more economical as compared to generation of DC.