Calculating unknown resistances
The current through the galvanometer (G) - a very sensitive ammeter, is reduced to zero by adjusting R_{4}. The bridge is then said to be balanced. When the bridge is balanced, the voltage at A is equal to the voltage at B and no current flows between A and B.
Hence V_{R1} = V_{R2}
therefore I_{1 }´ R_{1 }= I_{2} ´ R_{2} ------------- (1) (by Ohm's law)
Also V_{R3} = V_{R4}
therefore I_{1} ´ R_{3} = I_{2} ´ R_{4} ------------- (2)
Dividing (1) by (2)
Therefore the unknown resistor R_{3} = (all known values)
In calculations it is possible for any of the four resistors to be unknown. However, provided that the bridge is balanced, the theory remains the same and all that is required is to transpose the equation to find the unknown