Lesson_4.4_Printable_PPT

Lesson_4.4_Printable_PPT - Alternating Current A coil...

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Alternating Current A coil rotating in a magnetic field will have a current induced in it. 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. For each rotation of the coil, the direction of the induced emf, and hence current, changes. Such a generator is called an ac generator

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A rectangular coil of N turns and area A is 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 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 the induced emf will be a measure of the rate of change of flux linked with it. angle θ with the direction of the magnetic field B.
φ B = NAB cos ( ϖ t) B d E dt φ = - ( cos ) d NAB t dt ϖ = - sin ) A B t - - in( ) A B 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. ( N A B = - 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. sin( N A B t =

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The frequency f and the angular frequency ϖ are related such that = 2 π f Since E = NAB ϖ sin ω t, the maximum value of E occurs when sin ω t = 1. We will represent the maximum emf by E max ax NAB Using ω = 2 π f, t f, t he expression for the induced emf can now be written as E max = NAB ϖ . E (t) = E max sin(2 π f t) This induced voltage gives rise to an induced current given by I (t) = I max sin(2 π f t)
the voltage change with time for an ac As the coil begins to rotate, it cuts more field lines, the duced voltage increases and reaches a maximum when When the plane of the coil is perpendicular to B ( θ = 0), no change in flux occurs and the induced voltage is zero. induced voltage increases and reaches a maximum when the plane of the coil is parallel to B and the rate of change of flux is a maximum. As the coil continues to rotate, the number of field lines cut by the coil decreases and the induced voltage decreases to zero when the plane of the coil is perpendicular to B again. The end of the coil that was moving up now begins to move down and the induced voltage grows in the negative direction, reaches a negative maximum and then increases to zero. http://sun.ylojarvi.fi/java/pos/ganimaatio.htm

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Lesson_4.4_Printable_PPT - Alternating Current A coil...

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