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The relationship between the primary and secondary voltage in a transformer is fundamentally described by the equation Vp ÷ Vs = np ÷ ns. In this context, Vp represents the primary voltage, Vs denotes the secondary voltage, np is the number of turns in the primary coil, and ns is the number of turns in the secondary coil.

This equation illustrates the principle of electromagnetic induction and reflects how voltage levels change based on the turns ratio of the coils. When a transformer is designed with more turns on the primary side (np) compared to the secondary side (ns), it steps down the voltage; conversely, if there are more turns on the secondary side than the primary, it steps up the voltage. This ratio is essential for the functioning of a transformer, allowing it to regulate voltage levels efficiently for various applications in electrical systems.

The other options do not accurately represent the fundamental principles of transformer operation, so they do not correctly convey the relationship between voltage and the turns of the wire in a transformer.