Transformer Ratio
Voltage ratio equals the turns ratio.
Formula
Variables
Example
Steps voltage up or down
How it works
In an ideal transformer, the alternating magnetic flux in the core links both windings, so the induced voltage in each coil is proportional to how many turns it has. That is why the primary-to-secondary voltage ratio matches the primary-to-secondary turns ratio. This relationship comes from Faraday’s law of electromagnetic induction and assumes the transformer is operating efficiently with negligible losses.
When to use it
Use this formula when you know the number of turns on each winding and need to find the input or output voltage of an ideal transformer. It is especially useful in power distribution, electronics design, and lab problems involving step-up or step-down transformers.
Worked example, step by step
A transformer has 500 turns on the primary coil and 50 turns on the secondary coil. Given: Vp / Vs = Np / Ns Substitute the turns ratio: Vp / Vs = 500 / 50 = 10 So the primary voltage is 10 times the secondary voltage. If the primary voltage is 120 V: 120 / Vs = 10 Vs = 120 / 10 = 12 V Final answer: the secondary voltage is 12 V.
Common mistakes to avoid
- Reversing the primary and secondary quantities in the ratio
- Using this formula for DC circuits, where transformer action does not work
- Forgetting that the relationship is idealized and can differ slightly in real transformers due to losses
Did You Know?
Transformers have no moving parts yet quietly make the entire long-distance power grid possible.
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