Physics - Current Electricity Question with Solution | TestHub

Consider the circuit in the figure. When we attempt to reduce the circuit to an equivalent network containing the source $V$ and an equivalent resistor $R$, we find that nowhere is a resistor in series or parallel with another. We can, however, replace one portion of the network with an equivalent circuit, and this conversion will permit us, with ease, to reduce the combination of resistors to a single equivalent resistance. This conversion is called the wye-to-delta or delta-to-wye transformation.

Solving equations for $R_a$, $R_b$, and $R_c$ using Kirchhoff's laws:

$$R_a=\frac{R_1{R}_2}{R_1+R_2+R_3}$$

$$R_b=\frac{R_2{R}_3}{R_1+R_2+R_3}$$

$$R_c=\frac{R_1{R}_3}{R_1+R_2+R_3}$$