Hello, I had a question about finding input resistance. The question is shown in the attached "Input Resistance Problem Picture.pdf" file.

My attempt at solving the problem was to disconnect the signal source from the original circuit, and then attach a test independent voltage source where the signal source originally was. Then, I was to find an expression for "Rin". This expression would be my answer. I obtained: Rin = 1000 [Ω], as shown in the attached "Problem Work.pdf" file. The circuit including my test source is shown in the "Test Source Picture.pdf" file.

The correct answer for the problem is -43 [Ω]. I cannot figure out why this the correct answer.

Would anyone have any tips or advice for how to fix my mistakes in attempting this problem?

 

Bump

 

Your expression of iA is wrong. Also you cannot use formula of current divider here because there is current flowing through RF.
You can use nodal analysis to solve for iT.

 

Your expression of iA is wrong. Also you cannot use formula of current divider here because there is current flowing through RF.
You can use nodal analysis to solve for iT.

I was able to find the correct input resistance after using your advice. Thank you so much for the help!