Transformers (Circuits)

Electricity sent through power lines is transmitted with high voltages through long thick power lines because wires have a resistance that causes power loss at a rate proportional to the current squared. By transmitting at a high voltage, energy loss is minimized. Home appliances however operate at much lower voltages. Something is needed to convert the power to a high current, low voltage power that home appliances can use. This conversion from high voltage to low voltage, and vice versa, is accomplished by a transformer.

Background

Inductance

Currents can be induced (produced) by changing the current through a coil. This is due to the changing magnetic field [math]\displaystyle{ \textstyle (dB/dt) }[/math] produced by varying the current through the coil. We know from the Maxwell-Faraday Law of Maxwell's Equations:

[math]\displaystyle{ |emf| = \oint \overrightarrow{E}_{NC} \cdot d\overrightarrow{l} = \left | \frac{d\phi_{mag}}{dt} \right \vert }[/math]

Or that a changing magnetic field through an area produces a non-Coloumb electric field.

Mathematical Formulae

Before moving on to a discussion of the mathematics of transformers, here are some formulas it will be helpful to recall:

Circuits

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

See also

Faraday's Law

This will give you a general understanding of Faraday's Law, which is the basis behind transformer technology.

Inductance

Inductance is another property of an electrical conductor derived from Faraday's law.

Gauss's Flux Theorem

Changing the flux of a magnetic field around a coil will induce voltage.

Further reading

Books, Articles or other print media on this topic

External links

http://www.edisontechcenter.org/Transformers.html

References

Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 920). Danvers, Massachusetts: J. Wiley & sons.