hat is the Gain for this setup $(400-400)?$

$0\mathrm{.}93$ Units

What is the Gain for this new pair of coils $(400-200$ or $200-400)?$ Specify which one is on input and output.

Input $200-$ Output $400$

$0\mathrm{.}47$

What is the Gain after swapping the cables?

Input $400-$ Output $200$

$1\mathrm{.}82$ Units

What is the Gain here? Specify which one is on input and output.

Input $800-$ Output $200$

$=3\mathrm{.}63$

If induced voltage is directly proportional to the number of turns in a coil, what do you notice about the gain for the different coil setups? $($You should be able to show mathematically.$)$

Vout $/$ Vin $=$ Nout $/$ Nin

Describe what is happening here with these coils. Remember that they are NOT electrically connected, only sharing the same piece of iron.