Chapter 25, Problem 29A

To determine

To Explain: The effect on electric generator due to an increase in the length of wire of an armature.

Answer to Problem 29A

An increase in the conductor’s length results in a total increase in induced voltage.

Explanation of Solution

Introduction:

A device, which changes motive power (or mechanical energy) into electrical power (used in the external circuit), is called an electric generator. Electric generators work on the principle of electromagnetic induction.

Electromagnetic induction is a process of using a magnetic field to produce (or generate) voltage and current (in a complete circuit). Electromagnetic induction produces a voltage or EMF, i.e., electromagnetic force across the electrical conductor.

An armature is a piece of an electrical machine that carries electrical current. The windings of the armature are used to conduct AC even in the DC machines due to the action of the commentator that is used to reverse the direction of the current.

EMF is measured in volts and depends on the magnetic field, $B$ , length of a wire in the magnetic field, $l$ , plus the velocity of a wire in the field, $v$ . When, $B$ , $v$ and the direction of the length of a wire are mutually perpendicular, EMF is a product of these three quantities. Increasing the length of wire results in a total increase in induced potential difference because

  $EMF=Blv\left(\sin \theta \right)$

Conclusion:

When the length of the wire is increased, it also causes a net increase in the induced potential difference.