A step - down transformer is used for recharging the...

A step - down transformer is used for recharging the batteries of portable devices. The turns ratio $N_{2} / N_{1}$ for a particular transformer used in a CD player is 1:13. When used with 120. - V (rms) household service, the transformer draws an rms current of 250. mA. Find the (a) rms output voltage of the transformer and (b) power delivered to the CD player.

Key Concepts

Step-Down Transformer Operation

A step-down transformer is designed to reduce a higher input voltage to a lower output voltage by using electromagnetic induction between the primary and secondary windings. The transformer operates on the principle that the power (ignoring losses) remains approximately the same, so a decrease in voltage results in a corresponding increase in current, making it well suited for applications like battery charging in portable devices.

Transformer Turns Ratio

The turns ratio in a transformer is the ratio of the number of turns in the secondary winding to the number of turns in the primary winding. This ratio determines how the input voltage is scaled to produce the output voltage in an ideal transformer, with a lower ratio in a step?down transformer resulting in a reduced output voltage compared to the input.

RMS (Root Mean Square) Values

RMS values represent an effective or equivalent DC value for AC voltage or current, as they provide a meaningful measure for power calculations. In practical applications, using RMS values allows for consistent comparisons and calculations since RMS voltage and current measurements take into account the time-varying nature of alternating current.

AC Power Calculation

In AC circuits, power is typically calculated by multiplying the RMS voltage by the RMS current, assuming a purely resistive load where the voltage and current are in phase. This method provides the average power delivered to the load, enabling engineers to determine the performance of devices like transformers under operating conditions.

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