Question 2.45: Find the resistance between terminal XY of the bridge circui......
Find the resistance between terminal XY of the bridge circuit shown in Fig. 2.150, by using delta–star conversion.
Step-by-Step
Let us change the resistances forming a delta across terminals A, B, and C into equivalent star.
\mathrm{R}_{\mathrm{A}}=\frac{\mathrm{R}_{\mathrm{AB}} \times \mathrm{R}_{\mathrm{AC}}}{\mathrm{R}_{\mathrm{AB}}+\mathrm{R}_{\mathrm{BC}}+\mathrm{R}_{\mathrm{AC}}}=\frac{4 \times 6}{4+6+2}=\frac{24}{12}=2 \Omega\\ \begin{aligned} & \mathrm{R}_{\mathrm{B}}=\frac{\mathrm{R}_{\mathrm{AB}} \times \mathrm{R}_{\mathrm{BC}}}{\mathrm{R}_{\mathrm{AB}}+\mathrm{R}_{\mathrm{BC}}+\mathrm{R}_{\mathrm{AC}}}=\frac{4 \times 2}{12}=\frac{2}{3} \Omega \\ & \mathrm{R}_{\mathrm{C}}=\frac{\mathrm{R}_{\mathrm{BC}} \times \mathrm{R}_{\mathrm{AC}}}{\mathrm{R}_{\mathrm{AB}}+\mathrm{R}_{\mathrm{BC}}+\mathrm{R}_{\mathrm{AC}}}=\frac{2 \times 6}{12}=1 \Omega \end{aligned}The equivalent star–forming resistances are
By replacing the delta resistance into equivalent star resistance, the circuit is drawn as in Fig. 2.152
The resistances of the two parallel paths between N and D are 1+14=15 \Omega \text { and } \frac{2}{3}+10=\frac{32}{3} \Omega, respectively.
Total Resistance Network Terminal X and Y
=2+\frac{15 \times 10.67}{15+10.67}=8.23 \Omega
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