# Circuit Theory/Y Δ

!Circuit after Δ Y transformation of top bridge .. can now use
parallel/serial combinations rather than source injection to find
Thevenin\'s
resistanceThe
bridge circuit example was
solved with source injection, but could have been solved with a Y Δ
transformation. ![](Example23g.png "Example23g.png")\
The 5,2 and 3 ohm resistors form a Δ that could be transformed into a Y.
![](Wye-delta-2.svg)\
The equations are:

$$R_1 = \frac{R_bR_c}{R_a + R_b + R_c}, R_2 = \frac{R_aR_c}{R_a + R_b + R_c}, R_3 = \frac{R_aR_b}{R_a + R_b + R_c}$$

$$R_1 = \frac{5*2}{3 + 5 + 2}=1, R_2 = \frac{3*2}{3 + 5 + 2}=0.6, R_3 = \frac{3*5}{3 + 5 + 2}=1.5$$
Now Thevenin\'s resistance can be solved by parallel and serial
combinations:

$$R_{th} = \frac{1}{\frac{1}{8} + \frac{1}{10.6}} + 1.5 = 6.0591$$

Which is the same value found through source
injection.

