A generator / dynamo is a machine which produces alternating current energy from mechanical energy. It is one of the most important applications of the phenomenon of electromagnetic induction. The generator was designed originally by a Yugoslav scientist, because nothing is generated by the machine. It is an alter – nature converting one form of energy into another.
Principle: An A.C. generator / dynamo is based on the phenomenon of electromagnetic induction whenever amount of magnetic flux linked with a coil changes and is induced in the coil ti lasts coil continues. The direction of current induced is given by Fleming’s right hand rule.
Construction the essential parts of a dynamo are shown in fig. 1.
Armature ABCD is a rectangular armature coil. It consist of a large number of turns of insulated copper wire wound over a laminated soft iron core, I. The coil can be rotated about the central axis.
Field magnetic N and S are the pole pieces of a strong electromagnet in which the armature coil is rotated. Axis of rotation is perpendicular to the magnetic files lines. The magnetic fields are of the order of 1 to 2 tesla.
Slip rings R1 and R2 are tow hollow metallic rings, to which two ends of armature coil are connected. These rings rotate with the rotation of the coil.
Brushes. B1 and B2 are tow flexible metal plates or carbon rods. They are fixed and are kept in light contact with R1 and R2 respectively, the purpose of brooches is to pass on current from the armature coil to the external load resistance R.
Theory and working as the armature coil is rotated in the magnetic field angle θ between the field and normal to the coil changes continuously. Therefore, magnetic flux liked with the coil changes and induced in the coil.
To start with suppose the plane of the coil is perpendicular to the plane of the paper in which magnetic field is applied with AB at front and CD at the back? The amount of magnetic flux linked with the coil in this position is maximum. As the coil is rotated anticlockwise, AB moves inwards and CD moves outwards. The amount of magnetic flux linked with the coil changes according to Fleming’s right hand rule current induced in AB is from A to B and in CD it is from C to D. in the external circuit current flows from B2 to B1 fig 1 (a).
After half the rotation of the coil AB is at the back and CD is at the front therefore on rotation further AB moves outwards and CD moves inwards the current induced in AB is form B to A and in CD it is from D to C thorough external circuit current flows from B1 to B2
This is repeated induced current in the external circuit changes direction after every half rotation of the coil. Thence the current induced is alternating in nature.
To calculate the magnitude of induced, suppose
N = number of turns in the coil,
B = area enclosed by each turn of the coil
B = strength of magnetic flied
θ = angle which normal to the coil makes with B at any instant fig 4(c) 2.
∴ Magnetic flux linked with the coil in this position ∅ = N (b.A) = NBA cos θ = NBA cos w t
Where w is angular velocity of the coil.
As the coil is rotated, θ changes; therefore, magnetic flux ∅ linked with the coil changes and hence an is induced in the coil. At this instant t is e is the induced in the coil then
E – d ∅ / dt = - d / dt (NAB cos w t) = - NAB d / dt (cos w t) =- NAB (- sin w t )w
E = NAB w sin w t
The induced will be maximum when sin w t = maximum = 1
∴ E max = e0 = NAB w X 1
Put in, E = e0 sin w t
The variation of induced with time with position of the coil is shown in
The current supplied by the a.c generator is also sinusoidal. It is given by
I = e / R = e0 / R sin w t = i0 sin w t
Where i0 = e0 / R maximum value of current.
Note. Suppose to start with the plane of the coil is not perpendicular to the magnetic fids therefore at t O,θ ≠ 0. let θ = the phase angle. This is the angle which normal to the coil. Makes with the direction of B. the equation of induced in that case can be rewritten as e = e0 sin (w t +).
An a. e generator consists of a coil of 1000 turns each of area 100cm2 and rotating at an angular speed of 100 in a uniform magnet field of 3.6 X 10-2 find the peak and value of induced in the coil.
Here N = 1000, A = 10 cm2 = 100 X 10-4 m2 = 10-2 m2
V = 100 = 100 / 60 = 5/3
B = 3.6 X 10-2 T, e0 +? Ev = ?e0 = NAB w= NAB (2π v) = 1000 x 10-2 X 3.6 X 10-2 X 2 X 22/7 X 5/3 = 3.77 volt
Ev = e0 / 2 = 3.77 / 1.414 = 2.67 volt.
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