Calculating unknown resistances

The current through the galvanometer (G) - a very sensitive ammeter, is reduced to zero by adjusting R₄.  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   I₁ ´ R₁           =       I₂ ´ R₂ ------------- (1)  (by Ohm's law)

          Also           V_R3             =       V_R4

          therefore   I₁ ´ R₃        =       I₂ ´ R₄ ------------- (2)

Dividing (1) by (2) 

Therefore the unknown resistor  R₃  =     (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