The electric motor in a toy train requires a voltage of 3.0 V. Find the ratio of turns on the pr

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The electric motor in a toy train requires a voltage of 3.0...

The electric motor in a toy train requires a voltage of $3.0 \mathrm{V}$. Find the ratio of turns on the primary coil to turns on the secondary coil in a transformer that will step the 110 -V household voltage down to $3.0 \mathrm{V}$.

Key Concepts

Transformer

A transformer is an electrical device that transfers energy between two or more circuits through electromagnetic induction. It typically consists of two coils, known as the primary and secondary coils, wound around a magnetic core. The transformer operates based on the principle that a changing magnetic field in the primary coil induces an electromotive force (emf) in the secondary coil, thereby transferring energy from one circuit to another without a direct electrical connection.

Turns Ratio

The turns ratio of a transformer is the ratio of the number of windings (or turns) on the primary coil compared to the secondary coil. This ratio directly determines how the voltage is modified between the primary and secondary circuits according to the relation Vp/Vs = Np/Ns, where V is voltage and N is the number of turns. A higher turns ratio in a step-down transformer means that a high input voltage is converted to a lower output voltage.

Voltage Conversion

Voltage conversion in transformers is achieved by utilizing the inherent proportionality between the number of turns in the primary and secondary coils. In a step-down transformer, more turns on the primary coil relative to the secondary coil reduce the input voltage to a desired, lower value. This process allows equipment operating at a much lower voltage to be powered safely and efficiently from a higher voltage source.

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