Transformers — Question 4

Question 4

Maintaining the same flux ceiling requires constant voltage-to-frequency ratio

A transformer is designed for a sinusoidal 120-V rms primary at 60.0 Hz. Its turns and core area remain fixed. Ignore winding drops.

1. Find the rms voltage at 50.0 Hz that preserves the original peak core flux density.

2. If 120 V is retained at 50.0 Hz, find the peak-field ratio and compare it with a stated 10 percent allowable increase.

Question 4 - Solution

Maintaining the same flux ceiling requires constant voltage-to-frequency ratio

(a) Method and calculation

$$B_{\max}=\frac{V\sqrt2}{2\pi fNA}\Rightarrow B_{\max}\propto V/f.$$$$\boxed{V_{50}=120(50/60)=100\,V}.$$

(b) Interpretation and further calculation

$$B_{50}/B_{60}=(120/50)/(120/60)=1.20.$$$$\boxed{1.20>1.10\quad\text{so the stated field limit is exceeded}}.$$

Physical check

Frequency changes the flux swing even if rms voltage remains unchanged.