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The concept of the turns ratio is fundamental in understanding how transformers work. A turns ratio is simply a way of comparing the number of turns in the primary coil to the number of turns in the secondary coil. In the given exercise, the turns ratio is 1:8. This means that for every turn in the secondary coil, the primary coil has eight turns.

This ratio directly affects how voltages are transformed. A step-down transformer, like in the problem, reduces voltage from a higher level to a lower level. The turns ratio also plays a crucial role in determining how current changes between the primary and secondary coils.

• If the turns ratio is greater than 1, the transformer steps down voltage and steps up current.
• A direct correlation exists: more turns in the primary means greater primary voltage and lesser primary current and vice versa for the secondary.

Understanding the turns ratio helps in predicting how a transformer will affect both voltage and current in an electrical circuit.

The primary current in a transformer is the current that flows through the primary coil. This current is pivotal to the transformer's operation, as it creates the magnetic field that enables the voltage transformation. In our example, we are asked to find this primary current.

The relationship between the primary and secondary current can be described using the formula:\[\frac{I_p}{I_s} = \frac{N_s}{N_p}\]where:

• \( I_p \) is the primary current.
• \( I_s \) is the secondary current.
• \( N_s \) and \( N_p \) are the number of turns in the secondary and primary coils, respectively.

Using this equation, we can rearrange to solve for the primary current:\[I_p = I_s \times \frac{N_s}{N_p}\]Given that \( I_s = 1.6 \) A and \( \frac{N_s}{N_p} = \frac{1}{8} \), substituting these values, we find that:\[I_p = 1.6 \times \frac{1}{8} = 0.2 \text{ A}\]Thus, in this example, the primary current is 0.2 A. This illustrates how we can calculate the primary current when we know the turns ratio and the secondary current.

A step-down transformer is designed to decrease the voltage from a primary side to a secondary side. It does this through electromagnetic induction and a higher number of turns in the primary coil compared to the secondary coil. This configuration reduces the voltage output and increases the current output in the secondary coil.

Step-down transformers are commonly used in various applications, including adapters for household electronics to reduce the mains voltage to the safer levels needed for devices. In the exercise, the step-down transformer reduces the wall outlet voltage for the electric train to operate safely.

The efficiency of the transformer is one of its biggest advantages. While stepping down the voltage, it compensates by increasing the current on the secondary circuit, illustrated by the transformation equations:\[V_p \cdot I_p = V_s \cdot I_s\]where \( V \) represents voltage and \( I \) represents current for the respective coils.

• Primary Voltage \( V_p \) is reduced in the secondary circuit \( V_s \).
• Primary Current \( I_p \) is increased to Secondary Current \( I_s \).

This principle ensures energy conservation across the system, keeping power consistent while adjusting voltage and current levels to meet the specific needs of connected devices.