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Electromagnetic induction is a process where a change in magnetic field causes voltage to be induced in a conductor. This happens in transformers when the alternating current in the primary coil produces a changing magnetic field. This magnetic field then induces a voltage in the secondary coil. The key here is that the magnetic field must be varying for induction to occur.

Faraday's law of electromagnetic induction states that the induced voltage in a coil is proportional to the rate of change of the magnetic flux through the coil. This means that the faster the magnetic field changes, the greater the induced voltage.

In a transformer, the magnetic core guides the magnetic field from the primary to the secondary coil. The primary coil's alternating current creates a magnetic flux that changes in time, and this changing flux is what induces a voltage in the secondary coil.

Essentially, a transformer uses electromagnetic induction to "transform" or change the voltage from one level to another. This capability is crucial for transmitting electrical power efficiently over long distances.

The transformer voltage equation is a fundamental principle that helps us understand how transformers adjust voltages between the primary and secondary circuits. This equation is:\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \]where:

• \( V_s \) is the voltage across the secondary coil.
• \( V_p \) is the voltage across the primary coil.
• \( N_s \) is the number of turns in the secondary coil.
• \( N_p \) is the number of turns in the primary coil.

This equation shows that the voltage change across the transformer depends on the ratio of the number of turns in the secondary coil to the primary coil.

In the exercise, the primary voltage was given as \(25 \text{ V}\), with \(50\) turns in the primary and \(125\) in the secondary. Plugging these values into the transformer voltage equation gives us a secondary voltage: \( V_s = \left( \frac{N_s}{N_p} \right) \times V_p = 2.5 \times 25 = 62.5 \text{ V} \). This is how we calculate the secondary voltage using the transformer's loop ratio and initial primary voltage.

A step-up transformer is a type of transformer that increases voltage from the primary side to the secondary side. It is called "step-up" because it steps, or raises, the voltage to a higher level. This is essential in many applications, especially in the transmission of electricity over long distances where high voltage is necessary for efficient power movement.

The key characteristic of a step-up transformer is that the number of turns in the secondary coil \( N_s \) is greater than the number of turns in the primary coil \( N_p \). This is what allows the voltage to "step-up."

In the example given, we have a transformer with 50 turns in the primary coil and 125 turns in the secondary coil. This means the number of secondary turns is greater, indicating a step-up transformer. Using the equation \( \frac{N_s}{N_p} = 2.5 \), we confirm that the voltage in the secondary coil will indeed be higher than in the primary coil, calculated as \( 62.5 \text{ V} \). Step-up transformers play a critical role in power transmission systems, allowing electricity to travel efficiently with minimal losses.