Malla Reddy College of Engineering and Technology (MRCET)
Department of EEE ( 2017-18 )
Electrical Circuits EEE
R
X
+R
Y
=
...........(7)
R
Y
+R
Z
=
.............(8 )
R
Z
+R
X
=
.............(9)
By subtracting equation 8 from equation 7 given above, we get
𝑅𝑋 − 𝑅𝑍 =
𝑅1𝑅2 + 𝑅1𝑅3
𝑅1 + 𝑅2 + 𝑅3
−
𝑅2𝑅1 + 𝑅2𝑅3
𝑅1 + 𝑅2 + 𝑅3
… . … … . (10)
Then adding this equation to equation 9 above i.e. (R
Z
+R
X
) we get:
2𝑅𝑋 =
𝑅1𝑅2 + 𝑅1𝑅3 − 𝑅2𝑅1 − 𝑅2𝑅3 + 𝑅3𝑅1 + 𝑅3𝑅2
𝑅1 + 𝑅2 + 𝑅3
=
2𝑅1𝑅3
𝑅1 + 𝑅2 + 𝑅3
𝑅𝑋 =
𝑅1𝑅3
𝑅1 + 𝑅2 + 𝑅3
And in a similar way we can get:
𝑅𝑌 =
𝑅1𝑅2
𝑅1 + 𝑅2 + 𝑅3
𝑅𝑍 =
𝑅2𝑅3
𝑅1 + 𝑅2 + 𝑅3
Where RX, RY and RZ are the equivalent resistances in the Star connection corresponding to the
Delta connection with resistances R1, R2 and R3.
Dostları ilə paylaş: