The batteries in a portable CD player are recharged by a...

The batteries in a portable CD player are recharged by a unit that plugs into a wall socket. Inside the unit is a step-down transformer with a turns ratio of $1: 13 .$ The wall socket provides $120 \mathrm{~V}$. What voltage does the secondary coil of the transformer provide?

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Key Concepts

Transformer Operation

Transformers are devices that transfer electrical energy between two or more circuits through electromagnetic induction. They consist of primary and secondary coils wound around a magnetic core. When AC voltage is applied to the primary coil, it creates a magnetic field that induces a voltage in the secondary coil, allowing for the conversion of voltage levels without direct electrical connection.

Turns Ratio

The turns ratio of a transformer expresses the ratio of the number of turns in the primary coil to that in the secondary coil. This ratio determines the relationship between the input (primary) voltage and the output (secondary) voltage. Mathematically, the voltage across the coils is proportional to their turns, so V_secondary = (N_secondary / N_primary) × V_primary.

Voltage Transformation Calculation

In a step-down transformer, the secondary voltage is lower than the primary voltage. By applying the voltage transformation formula derived from the turns ratio, one can calculate the reduced secondary voltage. This concept is crucial in designing circuits that require a lower voltage level for safe and efficient operation.

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