The frequency of alternating current (AC) does not change in a transformer due to the fundamental principles of electromagnetic induction and the conservation of energy. A transformer is a device that transfers electrical energy between two or more coils through mutual electromagnetic induction. Let’s explore in detail why the frequency remains constant in a transformer:

1. **Principle of Electromagnetic Induction:**

**Faraday’s Law:**The operation of a transformer is governed by Faraday’s law of electromagnetic induction. According to this law, a change in magnetic flux through a coil induces an electromotive force (EMF) or voltage in the coil.**Primary and Secondary Coils:**In a transformer, there are two coils—the primary coil connected to the input voltage source and the secondary coil connected to the load. The changing magnetic flux in the primary coil induces a voltage in the secondary coil.

2. **Sinusoidal AC Voltage:**

**Input Voltage Characteristics:**Transformers are primarily designed to work with sinusoidal AC voltages. The input voltage applied to the primary coil is typically sinusoidal, representing a periodic variation in voltage over time.**Constant Frequency:**Since the input voltage is sinusoidal, the frequency remains constant throughout the AC cycle. The frequency of the AC power source is determined by the power generation system and is consistent across the power grid.

3. **Conservation of Energy:**

**Energy Transfer:**The primary purpose of a transformer is to transfer electrical energy from the primary coil to the secondary coil. The conservation of energy dictates that the energy input in the primary coil must be equal to the energy output in the secondary coil, neglecting losses.**No Energy Storage:**Transformers do not store energy but act as energy transfer devices. The energy transferred is in the form of a varying magnetic field that induces a voltage in the secondary coil.

4. **Ideal Transformer Model:**

**Ideal Transformer Assumptions:**In an ideal transformer model, it is assumed that there are no losses, and the transformer is 100% efficient. In such an idealized scenario, the frequency of the input AC signal is not altered during the transformation process.**Voltage and Current Transformation:**The transformer changes the voltage and current levels between the primary and secondary coils according to the turns ratio, but the frequency remains constant.

5. **Turns Ratio and Voltage Transformation:**

**Turns Ratio Relationship:**The turns ratio (N1/N2) of the transformer determines the voltage transformation between the primary (V1) and secondary (V2) coils. According to the turns ratio equation (V1/V2 = N1/N2), the voltage transformation is achieved without affecting the frequency.

6. **Inductive Reactance:**

**Inductive Reactance Relationship:**The inductive reactance in the transformer is proportional to the rate of change of magnetic flux, which is directly related to the frequency of the AC signal.**Constant Inductive Reactance:**In a transformer, the inductive reactance remains constant as long as the frequency is constant. This ensures that the transformer operates within its design parameters and does not introduce frequency-related variations.

7. **Power System Consistency:**

**Power Grid Standardization:**Power systems worldwide are standardized to operate at specific frequencies—commonly 50 Hz or 60 Hz. Transformers are designed and interconnected within these power systems, ensuring consistency in frequency across the grid.

8. **Core Saturation:**

**Core Saturation Effects:**At very high frequencies, transformer cores may experience saturation effects, causing an increase in core losses. However, within the standard power frequency range, core saturation is not a significant concern.

9. **Transformer Design:**

**Transformer Design Parameters:**Transformers are designed based on the specific frequency of the power system they are intended to operate in. The design parameters, such as core material and winding configuration, are optimized for the system frequency.

In summary, the frequency of the AC signal does not change in a transformer because of the principles of electromagnetic induction, the sinusoidal nature of AC voltage, conservation of energy, and the design considerations that ensure the transformer operates within the specified power system frequency.