# CBSE Class 12-science Answered

**Draw a labelled diagram of an a.c generator. Explain briefly its principle and working.**

## Principle of Ac Generator

One method to induce an emf or current in a loop is through a change in the loop orientation or a change in it’s effective area. As the coil rotates in a magnetic field B , the effective area of the loop (the face perpendicular to the field) is AcosӨ, where Ө is the angle between A and B. This method of producing a flux change is the principle of operation of a simple ac generator.

## A. C. Generator : Construction and Working

It consists of a coil mounted on a rotor shaft. The axis of rotation of the coil is perpendicular to the direction of the magnetic field. The coil called the armature is mechanically rotated in the uniform magnetic field by some external means . The rotation of the coil causes the magnetic flux through it to change, so an emf is induced in the coil . The ends of the coil are connected to an external circuit by means of slip rings and brushes.

Working

When the coil is rotated with the constant angular speed of *w* , the angle Ө between the magnetic field vector B and the area vector A of the coil at any instant t is Ө=*w*t(assuming Ө=0^{0}at t=0). As a result, the effective area of the coil exposed to the magnetic field lines changes with time, and the flux at any time is **ф**** _{B}=BAcosӨ=BAcoswt** From faraday’s law, the induced emf for the rotating coil of N turns is then,

**thus, the instantaneous value of the emf is**

*E*=-N×dф_{B}/dt = -NBA×d*coswt*∕dt*E*= NBA

*w*sin

*w*t.Where NBA

*w*is the maximum value of the emf,which occurs when sin

*w*t= +1 or -1. If we denote NBA

*w*as

*E*

_{0}, then

*E*=

*E*

_{0}sin

*w*t since the value of the sine function varies between +1 or -1, the sign, or polarity of the emf changes with time. The emf has its extremum value when Ө=90

^{0}or Ө=270, as the change of flux is greatest at these points. The direction current changes periodically and therefore the current is called alternating current.

The modern ac generator with a typical output capacity of 100 MW is a highly evolved machine.