Transformer Example Problem

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Kevin Starkey EMEC, Nick Christman, Aric Vyhmeister


Problem:

A step down transformer has a winding of  N_1 = 10 \text{ turns and } N_2 = 2 turns. (a) If the input voltage is 1200V, what is the resulting output voltage? (b) If the input and output currents are 5A \mbox{ and } 20A, respectively, what is the current loss due to the leakage inductance, i_{m}(t).

Figure 1: Model for an ideal transformer.
Figure 2: Magnetic circuit of an ideal transformer.


Solution:

a) By modifying equation 5-39 (Mohan 5-22) we can obtain an equation for the output voltage. That is,

 e_2 = \left( \frac{N_2}{N_1} \right) e_1 .


With the information provided we can now determine the output voltage:

  e_2 = \left( \frac{N_2}{N_1} \right) e_1 = \left( \frac{2}{10} \right) 1200V = 240V


b) From the figure above, we need to find the true value of current (i.e. the current that is not lost by leakage inductance). To accomplish this we will use equation 5-40 (Mohan 5-23) to obtain the value of i_{1}^{'}. That is,

i_{1}^{'} = \left( \frac{N_2}{N_1} \right) i_{2} = \left( \frac{2}{10} \right) 20A = 4A.

Now from equation 5-42 (Mohan 5-23) we can obtain the current loss due to the leakage inductance, which is

i_{m} = i_{1} - i_{1}^{'} = 5A - 4A = 1A.

Therefore, the current loss in our transformer is 1A, which means this specific transformer is very "leaky."