I am studying for a test, and I am stuck on a Linear Algebra problem that involves some knowledge of currents.
Here's the textbook problem:
The Wheatstone Bridge is used to determine an unknown resistance $R_3$ by adjusting a known resistance $R_1$, so that the measured current (in $r$) is zero. Determine the formula for $R_3$ using the linear system for the loop currents.
Here is the given image:
I know that the point of balance (when $r = 0$) is $R_3/R_1 = R_4/R_2$.
Thus, $R_3 = R_4R_1/R_2$.
Using Kirchoff's Current Law, I started getting a linear system.
$$I_1 R_1 - I_rr - I_3R_3 = 0$$
$$I_2 R_2 - I_4R_4+I_rr = 0$$
Which would also represent the point of balance.
Though, I don't know how to rearrange the linear system so that it equals $R_3$. Am I correct so far?