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Understanding coil resistance is crucial when dealing with transformers. Resistance in a wire is determined by how difficult it is for electricity to flow through it. This depends on several factors including the material's resistivity, the length of the wire, and its cross-sectional area.
In the case of transformers, each coil or winding has its own resistance. Primary and secondary coils often have different resistances because they have different numbers of turns. Resistance can be calculated using the formula \( R = \rho \frac{L}{A} \), where \( \rho \) is the resistivity of the material (copper in this case), \( L \) is the length of the wire, and \( A \) is the cross-sectional area.
For identical wires with the same diameter used in both coils, resistance is directly proportional to the length of the wire. Therefore, if one coil has a higher resistance, it generally has more turns (assuming each turn is the same length). As provided, the primary coil has a resistance of 56 Ω and the secondary 14 Ω, indicating the primary coil has more turns compared to the secondary.

The turns ratio of a transformer helps in determining how the voltage changes from primary to secondary coil. This ratio is the comparison of the number of turns in the primary coil to the number of turns in the secondary coil.
Given that both the primary and secondary coils use the same copper wire, their resistances can provide insight into their respective lengths, and thus, their turns. With \( R = \rho \frac{L}{A} \) and identical materials and design properties, the ratio of the resistances \( \frac{R_{\mathrm{p}}}{R_{\mathrm{s}}} \) is equal to the ratio of their turns \( \frac{N_{\mathrm{p}}}{N_{\mathrm{s}}} \).
For our problem, \( \frac{56}{14} = 4 \). This indicates that the number of turns in the primary coil is four times that in the secondary coil. Hence, the turns ratio \( \frac{N_{\mathrm{s}}}{N_{\mathrm{p}}} \) becomes \( \frac{1}{4} \), meaning the primary has 4 times more loops compared to the secondary.

Copper is widely used in electrical wiring due to its excellent conductivity and favorable physical properties. Key properties of copper that make it ideal for transformer coils include:

• High Conductivity: Copper's high ability to conduct electricity reduces energy loss due to resistance, making it efficient for transferring electricity in coils.
• Low Resistivity: The low resistivity of copper means it can carry more current across longer distances without heating up excessively, which is crucial in maintaining transformer efficiency.
• Ductility: Copper can be easily drawn into thin wires, necessary for winding the numerous turns in transformer coils.
• Thermal Conductivity: Effective thermal conductivity helps in dissipating heat generated by electrical resistance within the coils, thus preventing overheating.

These properties ensure that transformers can efficiently step up or step down voltage levels with minimal energy loss. In the problem, even though the resistance differed between coils, both coils benefited from using copper, ensuring reliable electrical performance.