T-TT conversion

Electricity and Magnetism Level 3

$R_1 = 2 \Omega$ , $R_2 = 3 \Omega$ and $R_3 = 6 \Omega$ are resistors interconnected with one common node while remained with 3 terminals named 1, 2 and 3 which are not externally connected. The equivalent circuit with same resultant resistances to replace them are resistors named $R_{12}$ , $R_{23}$ and $R_{31}$ of which each of them is connected to 2 among 3 terminals of exactly 3 distinct combinations or selections. What is the sum of resistances such that $R_{12} + R_{23} + R_{31}$ in $\Omega ?$

36 None of these choices

\frac{36}{11}

1 solution

Lu Chee Ket
Jan 8, 2016

This is a three to three sole conversion.

$R_{12} = \Large \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3} = \frac{6 + 18 + 12}{6} = 6$

$R_{23} = \Large \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1} = \frac{6 + 18 + 12}{2} = 18$

$R_{31} = \Large \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_2} = \frac{6 + 18 + 12}{3} = 12$

$R_{12} + R_{23} + R_{31} = 6 + 18 + 12 = 36$

Answer: $\boxed{36}$

Its just Star-Delta transformations .

Akshat Sharda - 5 years, 4 months ago

Yes, it's.

Lu Chee Ket - 5 years, 4 months ago

T-TT conversion

1 solution

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