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Transformers and the turns ratio equation

A transformer can change the size of an alternating voltage. A step-up transformer has more turns on the secondary coil than on the primary coil, so it increases the voltage. A step-down transformer has fewer turns on the secondary coil than on the primary coil, so it decreases the voltage.

The potential differences and the numbers of turns are linked by the turns ratio equation: Vp ÷ Vs = Np ÷ Ns. Vp and Vs are the potential differences across the primary and secondary coils in volts (V). Np and Ns are the numbers of turns on the primary and secondary coils. If the secondary coil has twice as many turns as the primary coil, the output voltage is twice the input voltage.

Worked example 1: a transformer has 12 V across 100 primary turns and gives 60 V from the secondary coil. Rearranging, Ns = Np × Vs ÷ Vp = 100 × 60 ÷ 12 = 500 turns. It is a step-up transformer.

Worked example 2: a transformer has 230 V across 1000 primary turns and 100 secondary turns. Vs = Vp × Ns ÷ Np = 230 × 100 ÷ 1000 = 23 V. It is a step-down transformer.

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