A transformer has 500 primary turns and 10 secondary turns. (a) If ΔVp is 120 V (rms), what is

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A transformer has 500 primary turns and 10 secondary turns....

A transformer has 500 primary turns and 10 secondary turns. (a) If $\Delta V_{p}$ is $120 \mathrm{~V}$ (rms), what is $\Delta V_{s}$ with an open circuit? (b) If the secondary now has a resistive load of $15 \Omega$, what are the currents in the primary and secondary?

Key Concepts

Transformer Turns Ratio

The transformer turns ratio is the relationship between the number of windings on the primary side and the secondary side of a transformer. This ratio is fundamental because it determines how the voltage and current values are scaled from one side to the other in an ideal transformer.

Voltage Transformation

In an ideal transformer, the voltage on the secondary side is directly proportional to the voltage on the primary side, multiplied by the ratio of the number of secondary turns to the number of primary turns. This principle allows one to calculate the expected output voltage when the transformer is operating under open-circuit conditions on the secondary side.

Current Transformation

The current transformation in an ideal transformer is inversely proportional to the turns ratio. This means that the primary current is adjusted relative to the secondary current based on the ratio of turns, ensuring that the power (ideally) remains conserved across the transformer under load conditions.

Ideal Transformer Model

An ideal transformer is a simplified model that assumes perfect magnetic coupling between the primary and secondary windings, no energy losses due to heat or resistance, and no leakage inductance. This model is useful for understanding the basic relationships between voltage, current, and turns ratio without the complexities of real-world imperfections.

Ohm's Law Application

Ohm's Law is a fundamental principle in electrical circuits stating that the current through a resistor is equal to the voltage across it divided by its resistance. It is applied here to determine the current in the transformer’s load when a resistive element is connected to the secondary winding.

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