Transformer Voltage Frequency Explained

The frequency of the induced voltage in a single-phase transformer remains constant primarily because transformers are static devices that operate based on the principle of electromagnetic induction, specifically mutual induction. Let's break down why this is the case and evaluate the given options.

Principle of Operation in Transformers

A transformer works by transferring electrical energy from one circuit to another through a varying magnetic field. When an alternating current (AC) flows through the primary winding, it creates a time-varying magnetic flux in the core. This changing flux links with the secondary winding and, according to Faraday's Law of Electromagnetic Induction, induces an electromotive force (EMF), or voltage, across the secondary winding. The fundamental equation for induced EMF is:

$$ E = -N \frac{d\Phi}{dt} $$

Where:

• E is the induced EMF (voltage).
• N is the number of turns in the winding.
• \(\Phi\) is the magnetic flux.
• \(\frac{d\Phi}{dt}\) is the rate of change of magnetic flux.

Crucially, the rate of change of flux is directly dependent on the frequency and magnitude of the AC supply voltage applied to the primary winding. If the supply voltage has a constant frequency (e.g., 50 Hz or 60 Hz), the magnetic flux will also vary at that same frequency, and consequently, the induced voltage in the secondary winding will have the same frequency.

Analyzing the Options

• Option 1: Leakage flux is less. Leakage flux affects the transformer's efficiency and voltage regulation but does not determine the frequency of the induced voltage. The frequency is dictated by the supply source.
• Option 2: Depends upon number of poles. The number of poles is a characteristic of rotating electrical machines like generators and motors, where it influences the generated voltage frequency based on rotational speed. Transformers are static devices and do not have rotating poles, making this irrelevant to their operating frequency.
• Option 3: Relative motion between coils is present. Relative motion between coils is the basis for induction in generators, where mechanical rotation causes the change in flux linkage. Transformers rely on mutual induction through a shared magnetic core, not mechanical relative motion.
• Option 4: There is no relative motion between coils. This statement accurately describes a transformer. Since there is no mechanical movement or rotation, the frequency of the induced voltage is solely dependent on the frequency of the AC input supply, which is typically constant. The alternating magnetic field causes the induction, not physical movement.

Conclusion

The frequency of the induced voltage in a single-phase transformer is constant because it directly matches the frequency of the AC supply voltage. This is maintained because the transformer is a static device; the induction process relies on the cyclical change in magnetic flux caused by the AC source, and there are no mechanical factors (like speed or relative motion) that could alter this frequency.