An exchange student from Canada will spend one semester in...

An exchange student from Canada will spend one semester in Germany, so she wants to purchase a transformer to step the $230-\mathrm{V}$ German power down to $120 \mathrm{~V}$ to power her hairdryer. (a) If the transformer's primary has 460 turns, how many should the secondary have? (b) She can save money with a transformer whose maximum primary current is $6.0 \mathrm{~A}$. If her hairdryer draws $12.5 \mathrm{~A}$, will this transformer work?

An exchange student from Canada will spend one semester in Germany, so she wants to purchase a transformer to step the $230-\mathrm{V}$ German power down to $120 \mathrm{~V}$ to power her hairdryer.
(a) If the transformer's primary has 460 turns, how many should the secondary have? (b) She can save money with a transformer whose maximum primary current is $6.0 \mathrm{~A}$. If her hairdryer draws $12.5 \mathrm{~A}$, will this transformer work?

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Key Concepts

Turns Ratio

The turns ratio is the relationship between the number of windings in the primary coil versus the secondary coil and directly determines the transformation of voltage. The ratio is given by the formula Vp/Vs = Np/Ns, meaning that the output voltage is proportional to the ratio of the secondary turns to the primary turns. This concept is crucial when designing or analyzing transformers to achieve a specific voltage conversion.

Power and Current Ratings

Transformers have specified power and current ratings which limit how much current can safely flow through the coils. The maximum current rating, particularly on the primary side, is important for ensuring the transformer operates safely and efficiently. Exceeding these ratings can lead to overheating, reduced performance, or even damage to the transformer, making it essential to match the transformer's capabilities with the load requirements.

Transformer Fundamentals

Transformers operate on the principle of electromagnetic induction, where a changing current in the primary coil produces a varying magnetic field that induces a voltage in the secondary coil. This fundamental concept allows electrical power to be transferred between two circuits without direct electrical connection, making transformers essential in adjusting voltage levels in power systems.

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