An arrangement of resistors which connect three nodes of a network in a ‘delta’ configuration is shown in Fig. (I) below. In circuit analysis it is sometimes convenient to replace the delta by the ‘star’ configuration illustrated in Fig. (II). Corresponding node voltages and node currents are identical in both circuits.
Prove that the resistance of each star branch equals (the product of adjacent delta resistances) ÷ (the sum of delta resistances). That is,