Understanding Autotransformers for Solving Homework Problems

[galaxy_twirl]

Homework Statement

I require some help for part i for now. :)

Homework Equations

N₁/N₂ = V₁/V₂
N₁/N₂ = I₂/I₁

The Attempt at a Solution

I tried doing the question like a normal transformer, but the result I got was vastly different from my teacher's. I also don't understand how my teacher could add 12V to the primary voltage of 120V to get 132V as the answer. I also don't understand a diagram he drew for the auto-transformer. Does anyone understand what this diagram mean?

Thanks! :)

 

[gneill]

Essentially an auto-transformer is a single coil with a "tap" along its length which divides it into two sections (or two coils if you will). The two sections are inductively mutually coupled.

You teacher took an ordinary two-coil transformer and connected its wires to form the equivalent of an auto-transformer.

 

[galaxy_twirl]

Essentially an auto-transformer is a single coil with a "tap" along its length which divides it into two sections (or two coils if you will). The two sections are inductively mutually coupled.

View attachment 75448

You teacher took an ordinary two-coil transformer and connected its wires to form the equivalent of an auto-transformer.

I see. Thank you. :) I am puzzled why the voltage of the secondary side can be higher than that of the primary side as the "main" transformer has turn ratios 120:12. I am also unable to see how the figure my teacher drew is related to the diagram you have shown above as they look quite different, although I know that your diagram is correct. ><

Is there a way to visualise this better?

Thank you. :)

 

[gneill]

Is there a way to visualise this better?

By making the connection shown, you're just "stacking" the secondary on top of the primary. The flux linkage still induces the same voltage on the secondary, but now it is added to the potential at the top of the primary due to where the secondary and primary conductors are connected.

 

[galaxy_twirl]

By making the connection shown, you're just "stacking" the secondary on top of the primary. The flux linkage still induces the same voltage on the secondary, but now it is added to the potential at the top of the primary due to where the secondary and primary conductors are connected.

View attachment 75545

OHHHHHH! This is awesome! I can totally understand it now! Thanks! :D:D You save my life! I'm going to have my exams in a few weeks' time and this autotransformer thing has been a bit abstract to me as it is rather new. Haha.

Just to confirm, if I were to draw the diagonal line the way other way (i.e. from bottom left to top-right), will the above setup become a step down autotransformer?

Thank you so much! :D

 

[gneill]

Not quite. Connect the tops of the windings (see figure). You can imagine the primary and secondary as having their labeled voltages and connect their wires accordingly to reinforce or oppose each other.

 

[galaxy_twirl]

Not quite. Connect the tops of the windings (see figure). You can imagine the primary and secondary as having their labeled voltages and connect their wires accordingly to reinforce or oppose each other.

View attachment 75546

I see. I think I will look at an example to check my understanding. :) Thank you once again.

Oh. Just wondering, is there a name for the diagram above, where you have a line connecting 2 sides of a transformer?

 

[gneill]

Oh. Just wondering, is there a name for the diagram above, where you have a line connecting 2 sides of a transformer?

Nothing specific comes to mind, other than it results in an autotransformer configuration.

 

[galaxy_twirl]

I see. Thank you. :) I will ask again if I run into any problems. I shall have to run for class now. Bye! :D

 

[galaxy_twirl]

Hi gneill. Back to this thread on autotransformers, may I ask, are there any good books or resources on autotransformers, especially on combining a 2-coil transformer into an autotransformer?

This is because I think I still do not really get the logic behind the 2-coil-to-1 configuration and hence would like to read up more on it.

Thanks! :D

 

[gneill]

Hi gneill. Back to this thread on autotransformers, may I ask, are there any good books or resources on autotransformers, especially on combining a 2-coil transformer into an autotransformer?

This is because I think I still do not really get the logic behind the 2-coil-to-1 configuration and hence would like to read up more on it.

Thanks! :D

I don't know of any particular books (at least I don't own one), but if you do a web search on "autotransformer tutorial" you should uncover quite a bit of material. For example:
http://www.faculty.umassd.edu/xtras/catls/resources/binarydoc/3525.ppt
A powerpoint presentation: http://www.faculty.umassd.edu/xtras/catls/resources/binarydoc/3525.ppt

All About Circuits ebook entry: The Autotransformer

 

[galaxy_twirl]

I don't know of any particular books (at least I don't own one), but if you do a web search on "autotransformer tutorial" you should uncover quite a bit of material. For example:
A powerpoint presentation: http://www.faculty.umassd.edu/xtras/catls/resources/binarydoc/3525.ppt

All About Circuits ebook entry: The Autotransformer

I see. Thank you! :)