Answer to Question #95879 in Electricity and Magnetism for Brandon

Question

Considering the below transformer U-Core:

https://upload.wikimedia.org/wikipedia/commons/8/81/U_core.png

When "Closing the U-Core" by placing a bar across the top (as per a recent experiment completed), what effect does changing the surface area of the bar in contact with one of the top segments (flat surface) of the U-Core. During the experiment one side of the U-Core - the secondary winding side was kept fully in contact with the bar "closing" the core, while the other side had varying overlaps of 10%, 50% and 100%. Voltage was increased from 0 --> 130V in steps of 10V. What appeared to happen was that the larger the overlap was the smaller the current in the primary current was and of course as the voltage increased so did the current. Is there any explanation to this - that the larger the surface area in contact with the primary winding results in a smaller current in the primary winding? Or any mathematics to tie into it. Any help greatly appreciated to help in my understanding.

Answer 1

First, we need to mention that it doesn't matter where the overlap is, because it plays a role of resistance in common circuits. In the core of the transformer the "current" is the magnetic flux, and the smaller the area of the overlap, the smaller the flux in the core.

According to Lenz's law,

$$I_{\text{induced}}=-\frac{\text{d}\Phi}{R\text{d}t},$$

i.e. the induced current is opposite to the change of magnetic flux. The current caused by the voltage source and flowing in the primary winding creates a magnetic flux $\Phi$. The expression we wrote above says that this current (call it main current) causes (induces) another current (counter-current) which flows in opposite direction and thus decreases the magnitude of the current which flows in the primary winding.

So if you conduct your measurements with 10% overlap (small magnetic flux), the induced current is small and its contribution to the reduction of the current caused by the applied voltage is small, therefore, the resulting current is high.

When you measured the total current in the primary coil with higher, 50 or 100% overlap, the magnetic flux was also high and the magnitude of the counter-current (induced one) was high, and it resulted in smaller total current. So, simply write

$$I_{\text{measured}}=I_\text{from voltage source}+I_\text{induced}=\\ \space\\=I_\text{from voltage source}-\frac{\text{d}\Phi}{R\text{d}t}.$$

Higher overlap results in higher magnetic flux which decreases the current you measure.