Rule 2: The resistance of any side of a ? network is equal to the sum of the Y network resistance, multiplied in pairs, divided by the opposite branch of the Y network.

Let us consider a bridge circuit show in the Figure.

Figure: Bridge Circuit

Find R_t at terminals a and d.

Step 1: Convert the Y network (b-e, e-c, e-d) to the equivalent ? network.

Using Rule 2:

R₁ =     (20) (20) + (20) (20)   + (20) (20) /20 =1200 /20 =60?     

R₂ =     1200 /20 =60?         

R₃ =     1200 /20 =60?         

Step 2: Now, we could redraw the Y circuit as a ? circuit and reconnect it to the original circuit in the Figure:

Figure: Y - Redrawn Circuit

Step 3: Reduce and simplify the circuit.  Notice that the 20 ? and 60? branches are in parallel in above Figure.  Refer to Figures Y - Redrawn Circuit and Steps to Simplify Redrawn Circuit for redrawing the circuit in every step below.

R_p =    R₁ R₄/ R₁ +    R₄ = (20) (60) /20 + 60 =1200 /80 =15?   

R_q =    R₁ R₅/ R₁ +    R₅ = (20) (60) /20 + 60 =1200 /80 =15?   

R_r =    R₃ (R_p +R_q) / R₃ (R_p +R_q) = (60) (15+15) /60 + 30 =1800 /90 =20?      

R_T = 20+20 = 40 ?    

Figure: Steps to Simplify Redrawn Circuit