A Step-Down Transformer. A transformer connected to a 120 V (rms) ac line is to supply 12.0 V (rms) to a portable electronic device. The load resistance in the secondary is 5.00 Ω. What should the ratio of primary to secondary turns of the transformer be?

Verified step by step guidance

1. Understand the basic principle of a transformer: A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of primary and secondary coils. The voltage across these coils is related by the turns ratio.
2. Identify the given values: The primary voltage \( V_p \) is 120 V (rms), and the secondary voltage \( V_s \) is 12.0 V (rms). The load resistance \( R_s \) in the secondary is 5.00 \( \Omega \).
3. Use the formula for the turns ratio of a transformer: The turns ratio \( \frac{N_p}{N_s} \) is given by \( \frac{V_p}{V_s} \). This formula relates the primary and secondary voltages to the number of turns in the primary \( N_p \) and secondary \( N_s \) coils.
4. Substitute the given values into the formula: \( \frac{N_p}{N_s} = \frac{120}{12} \). This will give you the ratio of the number of turns in the primary coil to the number of turns in the secondary coil.
5. Interpret the result: The calculated turns ratio will tell you how many times more turns the primary coil should have compared to the secondary coil to achieve the desired voltage transformation.

Key Concepts

Transformer Basics

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of primary and secondary coils, and it can either step up or step down voltage levels. The voltage change is determined by the ratio of the number of turns in the primary coil to the number of turns in the secondary coil.

Turn Ratio

The turn ratio of a transformer is the ratio of the number of turns in the primary coil to the number of turns in the secondary coil. This ratio determines how the input voltage is transformed into the output voltage. For a step-down transformer, the primary coil has more turns than the secondary coil, resulting in a lower output voltage compared to the input voltage.

RMS Voltage

RMS (Root Mean Square) voltage is a measure of the effective value of an alternating current (AC) voltage. It represents the equivalent DC voltage that would deliver the same power to a load. In the context of transformers, RMS values are used to describe both the input and output voltages, ensuring that the power calculations are accurate and consistent.