Transformers (Circuits)

claimed by vrivero3

A transformer makes use of Faraday's law and the ferromagnetic properties of an iron core to efficiently raise or lower AC voltages. It cannot increase power so that if the voltage is raised, the current is proportionally lowered and vice versa.

The Main Idea

From Faraday's law as well as conservation of energy we see that an ideal transformer the voltage ratio is equal to the turns ratio, and power in equals power out. Transformers uses both of these to convert from either high to low or low to high voltages.

A Mathematical Model

For a "step-down" transformer (one that converts from high to low voltage):

If a solenoid is built wrapping [math]\displaystyle{ {N}_{1} }[/math] turns around a hollow cylinder for the primary coil, and wrapping [math]\displaystyle{ {N}_{2} }[/math] turns around the outside of the secondary coil, and then connecting the primary coil to a an AC power supply, the emf that will develop in the secondary coil will be as follows:

The magnetic field made by the primary coil: [math]\displaystyle{ B = \frac{\mu_0IN_1}{d} }[/math] The cross-sectional area of the solenoid is A, so the emf in one turn of the secondary coil is: [math]\displaystyle{ \frac{AdB}{dt} }[/math] The total emf in the secondary coil is [math]\displaystyle{ {N}_{2} }[/math] times the emf in one turn, so the potential difference across the secondary coil is: [math]\displaystyle{ {N}_{2}A(mu_0{N}_{1}/d)dI/dt }[/math] The potential difference across the primary coil is [math]\displaystyle{ \frac{LdI}{dt} }[/math], where [math]\displaystyle{ L = \frac{mu_0AIN_1^2}{d} }[/math], so the potential difference across the primary coil is: [math]\displaystyle{ A(mu_0IN_1^2/d)dI/dt }[/math]

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

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See also

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Further reading

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External links

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References

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html