Complex Imaginary volumn 2 question 3

[danderson]

"There is a 16KV circuit with a load of 227 <31 degrees ohms. An electrician has been instructed to create a transformer so that the reflected impedance of the load mentioned is 100 <31 degrees ohms. What is the turns ratio that is required?"

Ok. The way you actually do this problem is straight forward. I understand that. However, how am I supposed to know that the 227 angle 31 degrees is the primary side? The way the question is worded, it sounds like 227 angle 31 degrees ohms is the secondary of a step up transformer. Looking at the solution, they used 227 angle 31 degrees ohms as the primary. Is this a poorly worded question, or am I missing something?

 

[power62]

Load is always connected to secondary side.

 

[danderson]

That's what I thought. That's why I assumed the load was 16KV and 227 angle 31 degrees. Is this problem trying to ask "A transformer must be designed with a primary voltage of 16KV to feed a load of 227 angle 31 ohms. What turns ratio is required to reflect back 100 angle 31 degrees ohms onto the primary?"

If so, I understand, and it is a very poorly worded problem.

 

[Silkworm]

Can see how this is confusing but the reflected impedance is always on the primary side. The only way to reduce the impedance using a transformer is by moving it from a higher voltage to a lower voltage. If the 227 ohm load was on the low side ( as you incorrectly assumed) then obviously we couldn't reduce it down to 100 by moving it over to the high voltage side since the turns ratio would need to be less than one. So you can quickly deduce the resistance given in the problem must be a primary referred quantity.

Also, loads are not always on the secondary side of a transformer. I've seen 6.9/.480kV transformers feeding Induction motors on the 6.9kv side and lighting load on the 480 side.

Hope this helps.

 

[virde]

If you notice, the reflected impedance simply means z11 in a Z matrix configuration, so you can most likely solve the problem using Z matrix via short and open circuit tests.

Alternatively, z11 just means the impedance looking from the primary side into the transformer. Obviously, the transimpedance (z12 and z21) of this assumed ideal transformer is 0.

Thus, using definition of a transformer, you have:

n = v2 / v1 = i1 / i2

n * n = v2 / i2 * i1 / v1 = z22 / z11 = 227<31 / 100<31 => n ~= 1.5.

The voltage seems irrelevant.