Example Problems with Transformers

Transformer Example

Kevin Starkey, 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 $5A\text{ and }20A$, respectively, what is the current loss due to the leakage inductance ($i_m(t)$.

Error creating thumbnail: File missing Figure 1: Model for an ideal transformer.

Error creating thumbnail: File missing 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 $i_1^{\text{'}}$. That is,

$i_1^{\text{'}}=\left(\frac{N_2}{N_1}\right)i_2=\left(\frac{2}{10}\right)20A=4A$.

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

$i_m=i_1-i_1^{\text{'}}=5A-4A=1A$.

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