Recently, I was interested in star-delta conversion formula and I wanted to test it on a 3-phase motor. First, I connected its second terminals together to have star configuration, and I measured each phase resistance which was 118 ohm, each. After that, I applied the star-delta conversion formula : 
For each phase, I got 354 ohm (theoretically). Then I connected motor as delta configuration, and I measured each phase which I got 78.6 ohm. Why such mismatch occured?
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2 Answers
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2 
simulate this circuit – Schematic created using CircuitLab
Figure 1. Simulation of resistance measurement using a 1 A source to generate 1 V/Ω allowing easy reading.
- (a) 118 Ω per individual winding.
- (b) 238 Ω when measuring between two phases of a star/wye connected motor.
- (c) 78.7 Ω when measuring between two phases of a delta connected motor.
- \$\begingroup\$ What are the purpose of these formulas? So, I cannot calculate the related phase in delta connection using the formula (A, B or C) \$\endgroup\$enis– enis2025-09-17 10:13:34 +00:00Commented Sep 17 at 10:13
- \$\begingroup\$ Those formulas are not about phase angle relationships - if that's what you're asking. They tell you about resistance and current flow. See if electronics-tutorials.ws/dccircuits/dcp_10.html helps. \$\endgroup\$Transistor– Transistor2025-09-17 12:50:43 +00:00Commented Sep 17 at 12:50
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0 When you measured the motor in star connection, the 118 Ω you saw is simply the resistance of a single coil. That’s a physical property of the winding and it doesn’t change whether you wire the motor in star or in delta.
The well-known “star–delta conversion” rule (where the delta resistance is three times the star resistance) is about making two equivalent networks of resistors behave the same at the terminals. It’s not saying that the actual motor windings magically change resistance when you reconfigure them.
In delta, each coil still has the same 118 Ω, but now your ohmmeter is measuring between two external terminals that are connected in a loop of three windings. What the meter sees is one coil directly between the terminals, and in parallel with the other two coils in series. That parallel path lowers the measured resistance, which is why you got about 78 Ω. In fact, that number is exactly what theory predicts, so your measurements are spot on.
