Find the resistance between terminals A and B in the electric circuit of below figure:

Concept:

Y(Wye) to Delta ‘or’ Delta to Y conversion technique is explained in the circuit below:

For a given Delta connection, the equivalent Wye connection will have resistances of values:

\({R_1} = \frac{R_bR_c}{{{R_a+R_b+R_c}}}\)

\({R_2} = \frac{R_aR_c}{{{R_a+R_b+R_c}}}\)

\({R_3} = \frac{R_aR_b}{{{R_a+R_b+R_c}}}\)

Application:

The given circuit is modified as shown below:

where R₁, R_2, and R₃ are calculated using Wye-Delta transformation as:

\({R_1} = \frac{50\times 40}{{{50+40+10}}}=20~Ω\)

\({R_2} = \frac{10\times 50}{{{50+40+10}}}=5~Ω \)

\({R_3} = \frac{10\times 40}{{{50+40+10}}}=4~Ω \)

The above circuit is redrawn as:

The resistance between terminals A and B is 19 Ω