Balance conditions for an a.c. bridge

The majority of famously knoen a.c. bridges are categorized as four-arm bridges & contain an arrangement of 4 impedances (in complex form, Z =R + or - jX) as presented in  diagram 27.1. As with the d.c. Wheat-stone bridge circuit, an a.c. bridge is understood to be ‘balanced’ when the current through the detector is 0 (i.e. when there is no current flowing b/w B and D of Figure 27.1). If the current through the detector is 0, then the current I1 flowing