Question

State the working principle of A.C. generator.

Accepted Answer

An AC generator is a machine that converts mechanical energy into electrical energy, generated as an alternating current sinusoidal output waveform

Principle:

When the coil moves through the magnetic field, an induced emf is generated in the coil. When the coil starts moving down the induced emf changes its direction.

The graph of induced emf is that of a sine curve. Because $ε_{ac} = ε_{0} sinωt$

Where $ε_{0}$ is the maximum value of induced EMF Let a coil of N turns be rotated at a speed $ω$ in the magnetic field $B$ . Let the area of the coil be A.

Magnetic flux $ϕ = \vec{B} \cdot \vec{A} = B \cdot Aωcosωt$

$E_{ind} = \frac{- dϕ}{dt} = B \cdot Aωsinωt$

For $N$ turns of the coil $E_{ind} = NB \cdot Asinωt$

Since $E_{\max} = NB \cdot Aω = ε_{0}$

$E_{ind} = ε_{0} sinωt$

Working of an a.c. generator

When the coil rotates in the magnetic field, then the orientation of the coil with respect to the magnetic field changes. It is measured by $θ = ω t$ , $θ$ is angle between the field vector and area vector when $θ = 0$ that is plane of the coil is perpendicular to the magnetic field. Therefore, field lines are perpendicular to the plane of the coil.

As the coil rotates angle $θ$ increases from $0 t o 90 °$ and induced EMF increases till it becomes maximum when the plane of the coil is parallel to the field.

When the coil rotates further $E_{ind}$ decrease plane of coil is perpendicular to the field $E_{ind} = 0$ when the plane of the coil is parallel to the field then $E_{ind} =$ Maximum.

The output of AC generator is

Embibe Experts Solutions for Chapter: Transient Current and Alternating Current, Exercise 1: West Bengal Board-2018

Embibe Experts Physics Solutions for Exercise - Embibe Experts Solutions for Chapter: Transient Current and Alternating Current, Exercise 1: West Bengal Board-2018

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