# Calculating resistance and reactance of an coil (motor winding)

I want to find out the resistance and the reactance of an motor coil. I can measure the magnitude of the current through the coil using a DMM.

For example, If the voltage across the coil is 230v ac and the current through the coil is 10A, Impedance, Z= 230/10 = 23 ohm. Now, how can I find the value of R and X where Z=R+jX?

Step:

1) Disconnect the power source from the motor. Use the DMM and set it in resistance mode to measure the DC resistance. Your resistance should be in the range of 0.1 ~ 50 ohm or so depending on the motor type.

2) Assuming that your power source is a sine wave at 230V, we know that

Vrms = Irms * |Z|

|Z| = sqrt(R^2 + X^2)

23 = sqrt(R^2 + X^2)

X^2 = 23^2 - R^2

X = sqrt(23^2 - R^2)

Since you know R, you can find X.

This, assuming that the motor is stalled when you have measured the current. If the motor is allowed to rotate, back emf comes in and this solution is no longer valid.

• I waned to find out the resistance and reactance of both the coils of single phase induction motor to calculate the required capacitance to use in series with the auxiliary winding. Back emf is induced in DC not in DC right? – user3717550 Apr 17 '15 at 19:47
• Any comment on back emf? – user3717550 Apr 24 '15 at 21:08
• Very late answer. Yes back-EMF occurs in AC motors too. AC motors also have high starting currents because at zero speed there is no back-EMF. As the motor speeds up back-EMF increases and current drops. – Transistor Aug 2 '17 at 19:38

R you can find by direct measurement with you multimeter by setting it to Resistance measurement.

You already calculated the magnetude of Z. There is then an simple formula you can use to determine x:

$$|Z| = \sqrt{ R^2 + X^2}$$ $$|Z|^2 = R^2 + X^2$$ $$X^2 = |Z|^2 - R^2$$

• If I measure the resistance directly with DMM, I'll get the DC resistance, right? Then should I multiply the value with 1.1 (not sure about this value) to get AC resistance (considering skin effect and others? – user3717550 Apr 17 '15 at 19:56
• At 60Hz the skin depth is normally much larger than the wire being used resulting in an very small difference. Unless you are working higher frequencies or with large conductors with large currents you can safely set AC resistance equal to DC resistance. – Password Apr 20 '15 at 12:11
• I have a LCR meter which can measure the inductance as well as ESR and DCR (dc resistance). I measured the values of a winding as below - ERS: 1.769 ohm DCR: 0.87 ohm What is the difference between these two? – user3717550 May 17 '15 at 16:31
• @user3717550 . Most probably the ESR represent the series resistance at a specified frequency. You'll have to look into the manual of the tester for what freq it would be. – Password May 19 '15 at 12:13