# Current Transformer flux and back emf with only one turn

Having looked for a number of days on the internet and studied to the best of my ability I am a little stumped on the current transformer flux linkage.

From my basic understanding of a voltage transformer, as a CT can be viewed as a step up VT.

A current in a coil of wire lags the voltage by 90 degrees due to inductive reactance. This has a flux linkage in an iron core which induces a back emf to a secondary coil of wire which corrects this phase displacement (+90 degrees). and produces a current in phase with the primary voltage.

My difficulty in understanding the CT is that they usually in my industry have only one turn on the primary which is therefore not an "inductor" so how is the secondary of a CT in phase with the primary when there is no initial 90 degree displacement?

Thanks

Hope this makes sense

Ben

• What do you mean when you say it's not an inductor? – Hearth Apr 5 at 19:51

You are confusing terms.

When you talk about/model an inductor with inductance $$\L\$$ $$v(t) =L \frac{\mathrm{d}i(t)} {\mathrm{d}t}$$

When you talk about/model a transformer $$\sum_k N_kI_k=Hl$$ for the $$\k\$$ windings on a transformer.

In this case the ampere-tuns balance in a transformer equivalent circuit $$Hl =\frac{Bl}{\mu}\propto I_0 \approx 0$$ can also be seen as the current through the magnetising -impedance or -branch of the transformer. Here Wikipedia correctly says for a two-winding transformer model:

With sinusoidal supply, core flux (and the current) lags the induced EMF by 90°.

However, this is only valid for $$\I_M\$$ and not for $$\I_C\$$ in the equivalent circuit below.

The circuit is valid for both VTs and each CT core.

• Well spotted @michael thanks for correction. – skvery Jul 29 at 13:28

A wire X in an electric circuit is fed through the ring iron core of the CT. That's the primary. Most of the magnetic flux around X bypasses the CT core, but the core catches a certain part of it. The perimeter of the ring times the average magnetization field strength in the core is = the current, so the magnetic flux through the core follows the changes in the current immediately.

CT disturbs neglibly the electric circuit. It disturbs but the effect probably cannot be noticed in the function of the circuit.

Let the core have a secondary winding like windings are constructed in ring core transformers. That secondary collects a voltage Vs which is proportional to the momentary changing rate of the current in X. That's a derivative and with sinusoidal current in X voltage Vs has 90 degrees phase lead when compared to X.

Let's connect to the secondary a load. For CT that load must have low resistance. That's because this way the current is determined by the inductive reactance of the secondary, the effect of the low resistance is neglible. The reactance causes perfect 90 degrees phase lag so the current in the secondary is in phase with the current in wire X.

Of course the current in the secondary cancels mostly the flux in the core, so the CT disturbs even less the current in X.

I think your actual error is to think X to be something else than the primary winding. It's a little loosely wound and it has not so many turns, but it's a winding which causes magnetic field and that magnetic field obeys Faraday's and Ampere's induction, so X has mutual inductance with the secondary.