Transformer Physics: Constant Frequency

A transformer operates on the principle of mutual electromagnetic induction. The alternating voltage applied to the primary coil ($V_p$) creates a time-varying magnetic flux ($\Phi$) in the core. This same time-varying flux links with the secondary coil, inducing an alternating voltage ($V_s$) across it.

The relationship between the induced voltage and the rate of change of flux is given by Faraday's Law: $E = -N \frac{d\Phi}{dt}$. Since the magnetic flux ($\Phi$) generated by the primary coil is the same flux that induces voltage in the secondary coil, the rate of change of flux ($\frac{d\Phi}{dt}$) is common to both. The frequency of the AC supply dictates the rate at which the flux changes. Therefore, the frequency of the voltage induced in the secondary winding is the same as the frequency of the voltage applied to the primary winding.

Analyzing Transformer Quantities

• Frequency: Remains the same. The transformer does not change the frequency of the AC supply.
• Voltage: Changes based on the turns ratio. The relationship is $ \frac{V_s}{V_p} = \frac{N_s}{N_p} $, where $N_s$ and $N_p$ are the number of turns in the secondary and primary coils, respectively.
• Current: Changes inversely to the turns ratio (ideally). The relationship is $ \frac{I_s}{I_p} = \frac{N_p}{N_s} $.
• Phase: The phase relationship between primary and secondary voltages can vary, but the frequency of both AC voltages is identical.

Thus, the frequency is the quantity that remains the same for the primary and secondary of a transformer.