《Single-Phase Transformers》.pdf

Single-Phase Transformers The transformer is one of the most widely used and useful electrical devices available. It can be used to transform an ac voltage or current in a circuit from one level to another and it can provide electrical isolation between circuits. By using transformers we can efficiently transmit electricity over a great distance at a high voltage and then reduce the voltage to safe level at the point of use (Q: Why is it more efficient to transmit electricity at a high voltage?). The voltage can then be further reduced and used to obtain the low voltage dc power supplies used in appliances such as computers, printers and CD players. The Ideal Transformer The transformer works by electromagnetic induction. If a sinusoidal ac voltage of is applied to a coil then it will produce a magnetic field where the flux will alternate at the same frequency as the voltage. Conversely if a coil is placed in an alternating magnetic field then a voltage will be induced in the coil that will alternate at the same frequency as the magnetic field. This is Faraday’s law of electromagnetic induction, which can be expressed as: dΦ dλ e N dt dt Where: e = voltage induced in the coil N = number of turns in the coil Φ = flux within the coil in Webbers (Wb) λ = flux linkage = NΦ (Wb) t = time in seconds If we now consider two coils that are closely coupled and we apply a sinusoidal voltage to one of the coils where the voltage is defined as: v V t cos( ) ω max Where: v = the instantaneous value of the voltage V = the peak value of the voltage max ω = 2лf The magnetic field produce