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Describe the physics of an electric generator with relevant equations ?

Added Mon, 27 Jul '15

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The electric generator is a machine for producing electric current. The electric generator or dynamo converts mechanical energy into electrical energy.

DC Generator

Principle

The generator is an application of electromagnetic induction. It works on the principle that when a wire is moved in a magnetic field, then the current is induced in the coil. A rectangular coil is made to rotate rapidly in the magnetic field between the poles of a horse shoe type magnet. When the coil rotates, it cuts the lines of magnetic force, due to which a current is produced in the generator coil. This current can be used to run the various electrical appliances.

Working

Let us suppose that the generator coil ABCD is initially in the horizontal position. As the coil rotates in the anticlockwise direction between the pole N and S of the magnet the side AB of the coil moves down cutting the magnetic lines of force near the N-pole of the magnet and side DC moves up, cutting the lines of force near the S-pole of the magnet. Due to this, induced current is produced in the sides AB and DC of the coil. On applying Fleming's right hand rule to the sides AB and DC of the coil we find that the currents in them are in the directions B to A and D to C respectively. Thus the induced currents in the two sides of the coil are in the same direction and we get an effective induced current in the direction BADC. Due to this the brush B1 becomes the positive pole and brush B2 becomes the negative pole of the generator.

After half revolution, the sides AB and DC of the coil will interchange their positions. The side AB will come on the right hand side and starts moving up whereas side DC will come on the left hand side and start moving down. But when sides of the coil interchange their positions, then the two commutator half rings R1 and R2 automatically change their contacts from one carbon brush to the other. Due to this change, the current keeps flowing in the same direction. Thus a DC generator supplies a current only in one direction.

1. The problem statement, all variables and given/known data

A generator uses a coil that has 100 turns and a 0.50-T magnetic field. The frequency of this generator is 60.0 Hz, and its emf has an rms value of 120 V. Assuming that each turn of the coil is a square (an approximation), determine the length of the wire from which the coil is made.

2. Relevant equations

Emf = NABwsin(wt) -- not sure if i should utilize sin(wt)?

and w = 2(pi)f

3. The attempt at a solution

I notice that the problem includes emf as an rms value. I figure that it is sq(2). Then, I figure out the w - the value is 377.

The problem setup so far is...

sq(2)*120V = (100 turns)(A)(0.50-T)(377) sin (377*.02) ---- i figured time, t by using the frequency T = 1/f equation.

Solving for A, I get A = .069 m^2. I then solve for the radius using A = (pi)r^2 and get r = .148 m. Then, I plug the r into L = 2(pi)r to get length. My answer is L = .931 m

Added Mon, 27 Jul '15

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