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. (a) What should the ratio of primary to secondary turns of the transformer be?

Verified step by step guidance

1. Identify the primary voltage (Vp) and the secondary voltage (Vs) from the problem. Here, Vp = 120 V and Vs = 12 V.
2. Use the transformer equation relating primary and secondary voltages with the number of turns on the primary (Np) and secondary (Ns) coils: \( \frac{V_p}{V_s} = \frac{N_p}{N_s} \).
3. Substitute the given values of Vp and Vs into the transformer equation to find the ratio \( \frac{N_p}{N_s} \).
4. Simplify the equation to solve for the ratio \( \frac{N_p}{N_s} \) which gives the required turns ratio of the transformer.
5. Verify that the calculated turns ratio makes sense in the context of a step-down transformer, where the primary voltage is higher than the secondary voltage, thus requiring more turns on the primary coil than on the secondary.

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, where the primary coil receives input voltage and the secondary coil delivers output voltage. The voltage transformation is directly related to the turns ratio of the coils.

Turns Ratio

The turns 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 voltage is transformed; a step-down transformer has a turns ratio less than one, meaning it reduces the voltage from primary to secondary. The relationship can be expressed as Vp/Vs = Np/Ns, where V is voltage and N is the number of turns.

Ohm's Law

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is expressed as V = IR, where V is voltage, I is current, and R is resistance. Understanding this law is crucial for analyzing the load on the secondary side of the transformer, as it helps determine the current drawn by the device.