Friday, 7 October 2011 , Posted by 12DEP11F1043 at 01:06

The general idea is to compute the impedance Ry at a terminal node of the Y circuit with impedances R'R'' to adjacent nodes in the Δ circuit by
$R_y = \frac{R'R''}{\sum R_\Delta}$
where RΔ are all impedances in the Δ circuit. This yields the specific formulae
$R_1 = \frac{R_aR_b}{R_a + R_b + R_c},$

$R_2 = \frac{R_bR_c}{R_a + R_b + R_c},$

$R_3 = \frac{R_aR_c}{R_a + R_b + R_c}.$

$R_\Delta = \frac{R_P}{R_\mathrm{opposite}}$
$R_a = \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_2},$
$R_b = \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_3},$
$R_c = \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1}.$