# Electrical – Identifying a multiple secondary unknown transformer

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# Background

I have a step-down isolated power transformer (EI-66×36) designed for 60Hz with one primary input Vp=110V and three secondary outputs : Vy=10V, Vb=26V, Vr=30V.

Unfortunately I don't know which wires is what.
I DON'T want to connect the transformer to the main line (not even in-series with a current limiter resistor) in order to figure out which coil is linked to what. I would rather try an invasive method using the theoretical knowledge, if possible.

By using the coils turns ratio equation E: Np/Ns=Vp/Vs=SQRT(Rp/Rs), where Np/Ns is the primary-to-secondary coil turns ratio, Vp/Vs is the primary-to-secondary coil voltage ratio, I deduced that on a step-down transformer the primary coil impedance is greater than any secondary coil impedance, ie. Rp/Rs > 1.

By measuring each coil impedance I found 4 pairs of wires as following:

• thick red wires with impedance of Rp=14.9 Ohm
• thin red wires with impedance of Rr=10.6 Ohm
• thin yellow wires with impedance of Ry=3.95 Ohm
• thin blue wires with impedance of Rb=1.67 Ohm

I concluded that the thick red wires must be connected to the primary coil and the others represents the secondary coils.

I've checked that there is no continuity (infinite resistance) between the secondary coils, which means that the secondary coils are completely isolated of each other.

# The problem

What bothers me is the fact that the above equation (E) doesn't seem to apply to this transformer and I don't understand why.

For instance the ration between the primary coil and the secondary coil identified by the thin red wires is: Vp/Vr=110/30=3.7 while the SQRT(Rp/Rr)=SQRT(14.9/10.6)=1.19, which is not as expected (ie. 3.7).

The same applies to the other ratios:

• Vp/Vb=110/26=4.23 while SQRT(Rp/Rb)=SQRT(14.9/1.67)=3, which is not as expected (ie. 4.23).
• Vp/Vy=110/10=11 while SQRT(Rp/Ry)=SQRT(14.9/3.95)=1.9, which is not as expected (ie. 11).

What am I doing wrong?