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whatisgoingon
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Homework Statement
I have to prove that RI = RSRP/(RS - RP) by circuit analysis.
The Attempt at a Solution
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So I tried to create a system of equations to do this:
For the first circuit using kirchhoffs rules:
V-IA(RS + RI) = 0 [1]
For the second circuit:
V-IBRS - IPRP = 0 [2]
V-IBRS - (IA)/2 * RI = 0 (It's IA/2 because of kirchhoffs rules regarding the junction therefore it's equivalent to the first circuit's I divided by 2) [3]
IB = IP + IA/2 [4]
First I solved for V for first 3 equations. Then for equation 4, i solved for IA/2 to make it easier for me, then I substituted it and tried to eliminate as much variables as I can by equating [1] and [2]. then whatever result I get for that, I then equate it to [3]. After doing this, I get
IB(2Rs + RI) = IP(2Rs + RI -RP)
Solving this using my head, I know I won't be able to prove the Ri equation. Any tips or other methods to do this?