Question

A bridge network ABCD has arms AB, BC, CD and DA of resistances 1, 1, 2 and 1 ohm respectively. If the detector AC has a resistance of 1 ohm, determine by star/delta transformation, the network resistance as viewed from the battery terminals.

Answer 1

As shown in Fig. , delta DAC has been reduced to its equivalent star.

R_D = (2 x 1)/(2 + 1 + 1) = 0.5Ω, R_A = 1/4 = 0.25Ω, R_C = 2/4 = 0.5Ω

Hence, the original network of Fig. is reduced to the one shown in Fig.. As seen, there are two parallel paths between points N and B, one of resistance 1.25 Ω and the other of resistance 1.5 Ω. Their combined resistance is

= (1.25 x 1.5)/(1.25 + 1.5) = 15/22Ω

Total resistance of the network between points D and B is

= 0.5 + 15/22 = 13/11Ω