Wheatstone bridge, prove converse.

AI Thread Summary
The discussion focuses on proving that a Wheatstone bridge is balanced if and only if the relationship R_x = R_3 (R_2/R_1) holds true. While demonstrating that a balanced bridge satisfies this equation is straightforward, the challenge lies in proving the converse. The user has attempted to use Kirchhoff's laws to approach the proof but has not been successful. The conversation highlights the difficulty in establishing the necessary conditions for balance in the Wheatstone bridge configuration. The need for a clear proof of the converse relationship remains unresolved.
SrEstroncio
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Homework Statement



You are given a standard Wheatstone bridge, prove that the bridge is balanced if and only if R_x = R_3 \frac{R_2}{R_1}. Subindexes depend on the names assigned to each resistance. Proving that if the bridge is balanced THEN the resistors satisfy said relationship is easy, I am having prouble proving that IF R_x = R_3 \frac{R_2}{R_1} then the bridge is balanced.

Homework Equations



500px-Wheatstonebridge.svg.png


The Attempt at a Solution



I have been trying to prove this using Kirchoff's laws around as many paths as i could find, but I am getting nowhere.
 
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