17 Alternating Current

AC Generator Simulator

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An AC generator, or alternator, is a device that converts mechanical energy into electrical energy by means of electromagnetic induction. At its core, the generator consists of a coil of wire that is made to rotate within a magnetic field. This magnetic field is usually produced by permanent magnets or electromagnets positioned so that their field lines pass through the area enclosed by the coil.

As the coil rotates, it cuts through the magnetic field lines. This motion causes the magnetic flux linkage through the coil to change over time. According to Faraday’s Law of Electromagnetic Induction, whenever there is a change in magnetic flux linkage through a circuit, an electromotive force (emf) is induced in the circuit. The faster the coil rotates or the stronger the magnetic field, the greater the rate of change of flux, and thus, the greater the induced emf.

The rotation causes the magnetic flux to vary in a sinusoidal manner, leading to an emf that also varies sinusoidally. This means the direction of the induced current reverses every half-turn, producing an alternating current (AC). The expression for the induced emf is typically given by: ϵ(t)=NBAωsin(ωt)

where N is the number of turns in the coil, B is the magnetic flux density, A is the area of the coil, ω is the angular velocity of rotation, and t is time.

To extract the current from the spinning coil without tangling wires, slip rings are connected to the ends of the coil. These rotate with the coil and maintain contact with carbon brushes, which allow the generated current to flow into an external circuit.

In essence, an AC generator works by continually rotating a coil within a magnetic field, causing a periodic change in magnetic flux that induces an alternating voltage. This principle is the foundation of electricity generation in power stations around the world.

AC Power with Half-Wave Rectification

As a means of visualising what happens to the potential difference, current and power dissipated in an alternating current circuit with half-wave rectification, I have created the interactive applet with all 3 graphs next to each other.

It should be easy for students to see that with half-wave rectification, the power dissipated is half that of a normal a.c. supply with the same peak p.d. and current.

Root-mean-square Currents

The concept of root-mean-square values for Alternating Currents is challenging if students are to relate the I-t graph with the Irms value directly.

They have to be brought through the 3 steps before arriving at the Irms value. This interactive applet allows them to go through step by step and compare several graphs at one time to see the relationship.

Through the interaction, students might be asked to observe that the Irms value is never higher than the peak Io.

For a complete sinusoidal current:

For a diode-rectified current:

In comparing the Irms of both currents, students can be asked to consider why the ratio of the values is not 2:1 or any other value, from energy considerations.

Worked on this earlier as I am the lead lecturer for this JC2 topic and am trying to integrate useful elements of blended learning. Do let me know in the comments if you have ideas or feedback that you would like to share.