Lesson_4.4

# Lesson_4.4 - Lesson 4.4 Alternating Current Circuits...

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Lesson 4.4 Alternating Current Circuits Alternating Current Generator An electric generator is a device which converts mechanical energy into electrical energy. The simplest practical generator consists of a rectangular coil rotating in a uniform magnetic field. The magnetic field is usually supplied by a permanent magnet or an electromagnet. Such a generator is called a rotating armature generator. When the coil rotates inside the magnetic field, the flux linked with coil changes continuously, and this induces an emf in the coil. The flux linked with the armature can also be changed by keeping it stationary inside a rotating magnetic field. Such a generator is called a rotating field generator. The magnetic field is generated by a current that passes through a coil of wire. When this coil is rotated, the magnetic field linked with the armature changes continuously, and this results in an induced emf in it. Almost all electric power is produced by alternating-current (ac) generators that are driven by rotating prime movers. Most of the prime movers are steam turbines (bottom right figure) whose thermal energy comes from either fossil or nuclear fuel. Combustion turbines are often used for the smaller units and in cases where gas or oil is the available fuel. Where water power is available from dams, hydroelectric ac generators are powered by hydraulic turbines. Small sites may also use diesel or gasoline engines to drive the generator, but these units are usually used only for standby generation or to provide electric power in remote areas.

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The theory of an AC Generator The figure shows a rectangular coil of N turns and area A placed in a magnetic field B caused by a permanent magnet. At any given time the normal to the plane of the coil makes an angle θ with the direction of the magnetic field B. The flux linked with the coil is φ B = NAB cos θ As the coil rotates, the angle θ is a function of time and can be written in terns of the angular frequency of rotation ϖ as θ = ϖ t φ B = NAB cos ( ϖ t) As the coil is rotated in the magnetic field, the flux linked with the coil changes, and this change in flux will induce an emf in the coil given by B d E dt φ = - ( cos ) d NAB t dt ϖ = - ( sin ) sin( ) N NAB t t AB = - - = When the coil moves up, if the induced emf is from a to b on the top side, when that side moves down, the emf will be from b to a. For each rotation of the coil, the direction of the induced emf, and hence the current generated by it, reverses. The number of times the direction of current reverses per second, which is the same as the number of rotations of the coil per second is called the frequency ( f ) of the ac. The ac used in the US for powering homes and industries has a frequency of 60 Hz. The direction of the current changes 60 times a second! The frequency f and the angular frequency are related such that
ϖ = 2 π f The maximum emf in the coil is d max = NAB ϖ . We will represent the maximum emf (amplitude) by

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Lesson_4.4 - Lesson 4.4 Alternating Current Circuits...

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