Transformers Calculation

November 7, 2008 – 6:11 am

A transformer can be viewed as a converter that can increase voltage and lower current, or vice versa. It only works when using AC.

The transformer is effectively a magnetic circuit. The transformer has two or more coils of wire wrapped about a common core.
transformer coil

The ideal relationship is:
transformer calculation

If a transformer has an iron core it will be shown with lines in the centre,
iron transformer

To deal with a transformer in a circuit analysis we need to pay attention to the polarity of the coils, and we may consider the inductance of each coil at times.

Consider the example below, from [Nilsson, pg. 450]. We want to find the power delivered to the 1ohm resistor. We will use the mesh current method,
transformer current

Next we can solve the remaining three equations and three unknown currents using a matrix approach,
transformer matrix

Finally we find the power in the resistor,
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